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Equation -x=4-3(3x-8)
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Equation x/9+x=-10/3
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Equation √(x^2-1)=2*x
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Equation 4(x-3)=x+6
- Express {x} in terms of y where:
- -6*x-20*y=8
- -9*x-15*y=-4
- 1*x+5*y=-11
- 12*x-14*y=20
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Identical expressions
- three *x^(- two)+ three *x^(- three)+ three *x^(- four)= two + two *x^- one
- 3 multiply by x to the power of ( minus 2) plus 3 multiply by x to the power of ( minus 3) plus 3 multiply by x to the power of ( minus 4) equally 2 plus 2 multiply by x to the power of minus 1
- three multiply by x to the power of ( minus two) plus three multiply by x to the power of ( minus three) plus three multiply by x to the power of ( minus four) equally two plus two multiply by x to the power of minus one
- 3*x(-2)+3*x(-3)+3*x(-4)=2+2*x-1
- 3*x-2+3*x-3+3*x-4=2+2*x-1
- 3x^(-2)+3x^(-3)+3x^(-4)=2+2x^-1
- 3x(-2)+3x(-3)+3x(-4)=2+2x-1
- 3x-2+3x-3+3x-4=2+2x-1
- 3x^-2+3x^-3+3x^-4=2+2x^-1
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Similar expressions
- 3*x^(-2)+3*x^(-3)+3*x^(-4)=2-2*x^-1
- 3*x^(-2)+3*x^(3)+3*x^(-4)=2+2*x^-1
- 3*x^(-2)+3*x^(-3)+3*x^(-4)=2+2*x^+1
- 3*x^(2)+3*x^(-3)+3*x^(-4)=2+2*x^-1
- 3*x^(-2)-3*x^(-3)+3*x^(-4)=2+2*x^-1
- 3*x^(-2)+3*x^(-3)-3*x^(-4)=2+2*x^-1
- 3*x^(-2)+3*x^(-3)+3*x^(4)=2+2*x^-1
3*x^(-2)+3*x^(-3)+3*x^(-4)=2+2*x^-1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
3 3 3 2 -- + -- + -- = 2 + - 2 3 4 x x x x
$$\left(\frac{3}{x^{2}} + \frac{3}{x^{3}}\right) + \frac{3}{x^{4}} = 2 + \frac{2}{x}$$
Rapid solution
[src]
_____________________________________________________________________________________________________________________________________
/ _________________
/ / ____
/ 5 / 25 5*\/ 30 5 5
I* / - - + 2*3 / - -- + -------- - ------------------------ + -----------------------------------------------------------------------
___________________________________________________________ / 2 \/ 64 64 _________________ ___________________________________________________________
/ | _________________ | / / ____ / | _________________ |
/ | / ____ | / / 25 5*\/ 30 / | / ____ |
/ |5 / 25 5*\/ 30 5 | / 8*3 / - -- + -------- / |5 / 25 5*\/ 30 5 |
/ |- + 2*3 / - -- + -------- - ------------------------| / \/ 64 64 4* / |- + 2*3 / - -- + -------- - ------------------------|
/ |4 \/ 64 64 _________________| / / |4 \/ 64 64 _________________|
/ | / ____ | / / | / ____ |
/ | / 25 5*\/ 30 | / / | / 25 5*\/ 30 |
/ | 8*3 / - -- + -------- | / / | 8*3 / - -- + -------- |
1 \/ | \/ 64 64 | \/ \/ | \/ 64 64 |
x1 = - - - --------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------
4 2 2
$$x_{1} = - \frac{1}{4} - \frac{\sqrt{\left|{- \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4}}\right|}}{2} - \frac{i \sqrt{- \frac{5}{2} - \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4 \sqrt{\left|{- \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4}}\right|}}}}{2}$$
_____________________________________________________________________________________________________________________________________
/ _________________
/ / ____
/ 5 / 25 5*\/ 30 5 5
I* / - - + 2*3 / - -- + -------- - ------------------------ + -----------------------------------------------------------------------
___________________________________________________________ / 2 \/ 64 64 _________________ ___________________________________________________________
/ | _________________ | / / ____ / | _________________ |
/ | / ____ | / / 25 5*\/ 30 / | / ____ |
/ |5 / 25 5*\/ 30 5 | / 8*3 / - -- + -------- / |5 / 25 5*\/ 30 5 |
/ |- + 2*3 / - -- + -------- - ------------------------| / \/ 64 64 4* / |- + 2*3 / - -- + -------- - ------------------------|
/ |4 \/ 64 64 _________________| / / |4 \/ 64 64 _________________|
/ | / ____ | / / | / ____ |
/ | / 25 5*\/ 30 | / / | / 25 5*\/ 30 |
/ | 8*3 / - -- + -------- | / / | 8*3 / - -- + -------- |
1 \/ | \/ 64 64 | \/ \/ | \/ 64 64 |
x2 = - - - --------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------
4 2 2
$$x_{2} = - \frac{1}{4} - \frac{\sqrt{\left|{- \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4}}\right|}}{2} + \frac{i \sqrt{- \frac{5}{2} - \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4 \sqrt{\left|{- \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4}}\right|}}}}{2}$$
_________________________________________________________________________________________________________________________________
/ _________________
/ / ____
/ 5 / 25 5*\/ 30 5 5
/ - - 2*3 / - -- + -------- + --------------------------------------------------------------------- + ------------------------
_________________________________________________________ / 2 \/ 64 64 _________________________________________________________ _________________
/ _________________ / / _________________ / ____
/ / ____ / / / ____ / 25 5*\/ 30
/ 5 / 25 5*\/ 30 5 / / 5 / 25 5*\/ 30 5 8*3 / - -- + --------
/ - + 2*3 / - -- + -------- - ------------------------ / 4* / - + 2*3 / - -- + -------- - ------------------------ \/ 64 64
/ 4 \/ 64 64 _________________ / / 4 \/ 64 64 _________________
/ / ____ / / / ____
/ / 25 5*\/ 30 / / / 25 5*\/ 30
/ 8*3 / - -- + -------- / / 8*3 / - -- + --------
1 \/ \/ 64 64 \/ \/ \/ 64 64
x3 = - - + ------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------
4 2 2
$$x_{3} = - \frac{1}{4} + \frac{\sqrt{- \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + \frac{5}{2} + \frac{5}{4 \sqrt{- \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4}}}}}{2}$$
_________________________________________________________________________________________________________________________________
/ _________________
/ / ____
/ 5 / 25 5*\/ 30 5 5
/ - - 2*3 / - -- + -------- + --------------------------------------------------------------------- + ------------------------
_________________________________________________________ / 2 \/ 64 64 _________________________________________________________ _________________
/ _________________ / / _________________ / ____
/ / ____ / / / ____ / 25 5*\/ 30
/ 5 / 25 5*\/ 30 5 / / 5 / 25 5*\/ 30 5 8*3 / - -- + --------
/ - + 2*3 / - -- + -------- - ------------------------ / 4* / - + 2*3 / - -- + -------- - ------------------------ \/ 64 64
/ 4 \/ 64 64 _________________ / / 4 \/ 64 64 _________________
/ / ____ / / / ____
/ / 25 5*\/ 30 / / / 25 5*\/ 30
/ 8*3 / - -- + -------- / / 8*3 / - -- + --------
1 \/ \/ 64 64 \/ \/ \/ 64 64
x4 = - - + ------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------
4 2 2
$$x_{4} = - \frac{\sqrt{- 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + \frac{5}{2} + \frac{5}{4 \sqrt{- \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4}}}}}{2} - \frac{1}{4} + \frac{\sqrt{- \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4}}}{2}$$
x4 = -sqrt(-2*(-25/64 + 5*sqrt(30)/64)^(1/3) + 5/(8*(-25/64 + 5*sqrt(30)/64)^(1/3)) + 5/2 + 5/(4*sqrt(-5/(8*(-25/64 + 5*sqrt(30)/64)^(1/3)) + 2*(-25/64 + 5*sqrt(30)/64)^(1/3) + 5/4)))/2 - 1/4 + sqrt(-5/(8*(-25/64 + 5*sqrt(30)/64)^(1/3)) + 2*(-25/64 + 5*sqrt(30)/64)^(1/3) + 5/4)/2
Sum and product of roots
[src]
sum
_____________________________________________________________________________________________________________________________________ _____________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________
/ _________________ / _________________ / _________________ / _________________
/ / ____ / / ____ / / ____ / / ____
/ 5 / 25 5*\/ 30 5 5 / 5 / 25 5*\/ 30 5 5 / 5 / 25 5*\/ 30 5 5 / 5 / 25 5*\/ 30 5 5
I* / - - + 2*3 / - -- + -------- - ------------------------ + ----------------------------------------------------------------------- I* / - - + 2*3 / - -- + -------- - ------------------------ + ----------------------------------------------------------------------- / - - 2*3 / - -- + -------- + --------------------------------------------------------------------- + ------------------------ / - - 2*3 / - -- + -------- + --------------------------------------------------------------------- + ------------------------
___________________________________________________________ / 2 \/ 64 64 _________________ ___________________________________________________________ ___________________________________________________________ / 2 \/ 64 64 _________________ ___________________________________________________________ _________________________________________________________ / 2 \/ 64 64 _________________________________________________________ _________________ _________________________________________________________ / 2 \/ 64 64 _________________________________________________________ _________________
/ | _________________ | / / ____ / | _________________ | / | _________________ | / / ____ / | _________________ | / _________________ / / _________________ / ____ / _________________ / / _________________ / ____
/ | / ____ | / / 25 5*\/ 30 / | / ____ | / | / ____ | / / 25 5*\/ 30 / | / ____ | / / ____ / / / ____ / 25 5*\/ 30 / / ____ / / / ____ / 25 5*\/ 30
/ |5 / 25 5*\/ 30 5 | / 8*3 / - -- + -------- / |5 / 25 5*\/ 30 5 | / |5 / 25 5*\/ 30 5 | / 8*3 / - -- + -------- / |5 / 25 5*\/ 30 5 | / 5 / 25 5*\/ 30 5 / / 5 / 25 5*\/ 30 5 8*3 / - -- + -------- / 5 / 25 5*\/ 30 5 / / 5 / 25 5*\/ 30 5 8*3 / - -- + --------
/ |- + 2*3 / - -- + -------- - ------------------------| / \/ 64 64 4* / |- + 2*3 / - -- + -------- - ------------------------| / |- + 2*3 / - -- + -------- - ------------------------| / \/ 64 64 4* / |- + 2*3 / - -- + -------- - ------------------------| / - + 2*3 / - -- + -------- - ------------------------ / 4* / - + 2*3 / - -- + -------- - ------------------------ \/ 64 64 / - + 2*3 / - -- + -------- - ------------------------ / 4* / - + 2*3 / - -- + -------- - ------------------------ \/ 64 64
/ |4 \/ 64 64 _________________| / / |4 \/ 64 64 _________________| / |4 \/ 64 64 _________________| / / |4 \/ 64 64 _________________| / 4 \/ 64 64 _________________ / / 4 \/ 64 64 _________________ / 4 \/ 64 64 _________________ / / 4 \/ 64 64 _________________
/ | / ____ | / / | / ____ | / | / ____ | / / | / ____ | / / ____ / / / ____ / / ____ / / / ____
/ | / 25 5*\/ 30 | / / | / 25 5*\/ 30 | / | / 25 5*\/ 30 | / / | / 25 5*\/ 30 | / / 25 5*\/ 30 / / / 25 5*\/ 30 / / 25 5*\/ 30 / / / 25 5*\/ 30
/ | 8*3 / - -- + -------- | / / | 8*3 / - -- + -------- | / | 8*3 / - -- + -------- | / / | 8*3 / - -- + -------- | / 8*3 / - -- + -------- / / 8*3 / - -- + -------- / 8*3 / - -- + -------- / / 8*3 / - -- + --------
1 \/ | \/ 64 64 | \/ \/ | \/ 64 64 | 1 \/ | \/ 64 64 | \/ \/ | \/ 64 64 | 1 \/ \/ 64 64 \/ \/ \/ 64 64 1 \/ \/ 64 64 \/ \/ \/ 64 64
- - - --------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------ + - - - --------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------ + - - + ------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------ + - - + ------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------
4 2 2 4 2 2 4 2 2 4 2 2
$$\left(- \frac{\sqrt{- 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + \frac{5}{2} + \frac{5}{4 \sqrt{- \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4}}}}}{2} - \frac{1}{4} + \frac{\sqrt{- \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4}}}{2}\right) + \left(\left(- \frac{1}{4} + \frac{\sqrt{- \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + \frac{5}{2} + \frac{5}{4 \sqrt{- \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4}}}}}{2}\right) + \left(\left(- \frac{1}{4} - \frac{\sqrt{\left|{- \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4}}\right|}}{2} - \frac{i \sqrt{- \frac{5}{2} - \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4 \sqrt{\left|{- \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4}}\right|}}}}{2}\right) + \left(- \frac{1}{4} - \frac{\sqrt{\left|{- \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4}}\right|}}{2} + \frac{i \sqrt{- \frac{5}{2} - \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4 \sqrt{\left|{- \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4}}\right|}}}}{2}\right)\right)\right)$$
=
_________________________________________________________ ___________________________________________________________
/ _________________ / | _________________ |
/ / ____ / | / ____ |
/ 5 / 25 5*\/ 30 5 / |5 / 25 5*\/ 30 5 |
-1 + / - + 2*3 / - -- + -------- - ------------------------ - / |- + 2*3 / - -- + -------- - ------------------------|
/ 4 \/ 64 64 _________________ / |4 \/ 64 64 _________________|
/ / ____ / | / ____ |
/ / 25 5*\/ 30 / | / 25 5*\/ 30 |
/ 8*3 / - -- + -------- / | 8*3 / - -- + -------- |
\/ \/ 64 64 \/ | \/ 64 64 |
$$-1 - \sqrt{\left|{- \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4}}\right|} + \sqrt{- \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4}}$$
product
/ _____________________________________________________________________________________________________________________________________\ / _____________________________________________________________________________________________________________________________________\ / _________________________________________________________________________________________________________________________________\ / _________________________________________________________________________________________________________________________________\ | / _________________ | | / _________________ | | / _________________ | | / _________________ | | / / ____ | | / / ____ | | / / ____ | | / / ____ | | / 5 / 25 5*\/ 30 5 5 | | / 5 / 25 5*\/ 30 5 5 | | / 5 / 25 5*\/ 30 5 5 | | / 5 / 25 5*\/ 30 5 5 | | I* / - - + 2*3 / - -- + -------- - ------------------------ + ----------------------------------------------------------------------- | | I* / - - + 2*3 / - -- + -------- - ------------------------ + ----------------------------------------------------------------------- | | / - - 2*3 / - -- + -------- + --------------------------------------------------------------------- + ------------------------ | | / - - 2*3 / - -- + -------- + --------------------------------------------------------------------- + ------------------------ | | ___________________________________________________________ / 2 \/ 64 64 _________________ ___________________________________________________________ | | ___________________________________________________________ / 2 \/ 64 64 _________________ ___________________________________________________________ | | _________________________________________________________ / 2 \/ 64 64 _________________________________________________________ _________________ | | _________________________________________________________ / 2 \/ 64 64 _________________________________________________________ _________________ | | / | _________________ | / / ____ / | _________________ | | | / | _________________ | / / ____ / | _________________ | | | / _________________ / / _________________ / ____ | | / _________________ / / _________________ / ____ | | / | / ____ | / / 25 5*\/ 30 / | / ____ | | | / | / ____ | / / 25 5*\/ 30 / | / ____ | | | / / ____ / / / ____ / 25 5*\/ 30 | | / / ____ / / / ____ / 25 5*\/ 30 | | / |5 / 25 5*\/ 30 5 | / 8*3 / - -- + -------- / |5 / 25 5*\/ 30 5 | | | / |5 / 25 5*\/ 30 5 | / 8*3 / - -- + -------- / |5 / 25 5*\/ 30 5 | | | / 5 / 25 5*\/ 30 5 / / 5 / 25 5*\/ 30 5 8*3 / - -- + -------- | | / 5 / 25 5*\/ 30 5 / / 5 / 25 5*\/ 30 5 8*3 / - -- + -------- | | / |- + 2*3 / - -- + -------- - ------------------------| / \/ 64 64 4* / |- + 2*3 / - -- + -------- - ------------------------| | | / |- + 2*3 / - -- + -------- - ------------------------| / \/ 64 64 4* / |- + 2*3 / - -- + -------- - ------------------------| | | / - + 2*3 / - -- + -------- - ------------------------ / 4* / - + 2*3 / - -- + -------- - ------------------------ \/ 64 64 | | / - + 2*3 / - -- + -------- - ------------------------ / 4* / - + 2*3 / - -- + -------- - ------------------------ \/ 64 64 | | / |4 \/ 64 64 _________________| / / |4 \/ 64 64 _________________| | | / |4 \/ 64 64 _________________| / / |4 \/ 64 64 _________________| | | / 4 \/ 64 64 _________________ / / 4 \/ 64 64 _________________ | | / 4 \/ 64 64 _________________ / / 4 \/ 64 64 _________________ | | / | / ____ | / / | / ____ | | | / | / ____ | / / | / ____ | | | / / ____ / / / ____ | | / / ____ / / / ____ | | / | / 25 5*\/ 30 | / / | / 25 5*\/ 30 | | | / | / 25 5*\/ 30 | / / | / 25 5*\/ 30 | | | / / 25 5*\/ 30 / / / 25 5*\/ 30 | | / / 25 5*\/ 30 / / / 25 5*\/ 30 | | / | 8*3 / - -- + -------- | / / | 8*3 / - -- + -------- | | | / | 8*3 / - -- + -------- | / / | 8*3 / - -- + -------- | | | / 8*3 / - -- + -------- / / 8*3 / - -- + -------- | | / 8*3 / - -- + -------- / / 8*3 / - -- + -------- | | 1 \/ | \/ 64 64 | \/ \/ | \/ 64 64 | | | 1 \/ | \/ 64 64 | \/ \/ | \/ 64 64 | | | 1 \/ \/ 64 64 \/ \/ \/ 64 64 | | 1 \/ \/ 64 64 \/ \/ \/ 64 64 | |- - - --------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------|*|- - - --------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------|*|- - + ------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------|*|- - + ------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------| \ 4 2 2 / \ 4 2 2 / \ 4 2 2 / \ 4 2 2 /
$$\left(- \frac{1}{4} - \frac{\sqrt{\left|{- \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4}}\right|}}{2} - \frac{i \sqrt{- \frac{5}{2} - \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4 \sqrt{\left|{- \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4}}\right|}}}}{2}\right) \left(- \frac{1}{4} - \frac{\sqrt{\left|{- \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4}}\right|}}{2} + \frac{i \sqrt{- \frac{5}{2} - \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4 \sqrt{\left|{- \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4}}\right|}}}}{2}\right) \left(- \frac{1}{4} + \frac{\sqrt{- \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + \frac{5}{2} + \frac{5}{4 \sqrt{- \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4}}}}}{2}\right) \left(- \frac{\sqrt{- 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + \frac{5}{2} + \frac{5}{4 \sqrt{- \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4}}}}}{2} - \frac{1}{4} + \frac{\sqrt{- \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4}}}{2}\right)$$
=
/ _____________________________________________________________________________________________________________________________________\ / _____________________________________________________________________________________________________________________________________\
| / | 1 | | | / | 1 | |
| / 5*|-------------------------------------------------------------------| | | / 5*|-------------------------------------------------------------------| |
| / | _________________________________________________________| | | / | _________________________________________________________| |
/ _________________________________________________________________________________________________________________________________\ / _________________________________________________________________________________________________________________________________ \ | / | / _________________ | | | / | / _________________ | |
| / _________________ | | / _________________ | | / | / / ____ | | | / | / / ____ | |
| / / ____ | | / / ____ | | / | / 5 / 25 5*\/ 30 5 | | | / | / 5 / 25 5*\/ 30 5 | |
| / 5 / 25 5*\/ 30 5 5 | | / 5 / 25 5*\/ 30 5 5 | | / | / - + 2*3 / - -- + -------- - ------------------------ | | | / | / - + 2*3 / - -- + -------- - ------------------------ | |
| / - - 2*3 / - -- + -------- + --------------------------------------------------------------------- + ------------------------ | | / - - 2*3 / - -- + -------- + --------------------------------------------------------------------- + ------------------------ | | / | / 4 \/ 64 64 _________________ | | | / | / 4 \/ 64 64 _________________ | |
| _________________________________________________________ / 2 \/ 64 64 _________________________________________________________ _________________ | | / 2 \/ 64 64 _________________________________________________________ _________________ _________________________________________________________| | ___________________________________________________________ / | / / ____ | | | ___________________________________________________________ / | / / ____ | |
| / _________________ / / _________________ / ____ | | / / _________________ / ____ / _________________ | | / | _________________ | / _________________ | / / 25 5*\/ 30 | | | / | _________________ | / _________________ | / / 25 5*\/ 30 | |
| / / ____ / / / ____ / 25 5*\/ 30 | | / / / ____ / 25 5*\/ 30 / / ____ | | / | / ____ | / / ____ | / 8*3 / - -- + -------- | | | / | / ____ | / / ____ | / 8*3 / - -- + -------- | |
| / 5 / 25 5*\/ 30 5 / / 5 / 25 5*\/ 30 5 8*3 / - -- + -------- | | / / 5 / 25 5*\/ 30 5 8*3 / - -- + -------- / 5 / 25 5*\/ 30 5 | | / |5 / 25 5*\/ 30 5 | / 5 / 25 5*\/ 30 5 |\/ \/ 64 64 | | | / |5 / 25 5*\/ 30 5 | / 5 / 25 5*\/ 30 5 |\/ \/ 64 64 | |
| / - + 2*3 / - -- + -------- - ------------------------ / 4* / - + 2*3 / - -- + -------- - ------------------------ \/ 64 64 | | / 4* / - + 2*3 / - -- + -------- - ------------------------ \/ 64 64 / - + 2*3 / - -- + -------- - ------------------------ | | / |- + 2*3 / - -- + -------- - ------------------------| I* / - - + 2*3 / - -- + -------- - ------------------------ + ----------------------------------------------------------------------- | | / |- + 2*3 / - -- + -------- - ------------------------| I* / - - + 2*3 / - -- + -------- - ------------------------ + ----------------------------------------------------------------------- |
| / 4 \/ 64 64 _________________ / / 4 \/ 64 64 _________________ | | / / 4 \/ 64 64 _________________ / 4 \/ 64 64 _________________ | | / |4 \/ 64 64 _________________| / 2 \/ 64 64 _________________ 4 | | / |4 \/ 64 64 _________________| / 2 \/ 64 64 _________________ 4 |
| / / ____ / / / ____ | | / / / ____ / / ____ | | / | / ____ | / / ____ | | / | / ____ | / / ____ |
| / / 25 5*\/ 30 / / / 25 5*\/ 30 | | / / / 25 5*\/ 30 / / 25 5*\/ 30 | | / | / 25 5*\/ 30 | / / 25 5*\/ 30 | | / | / 25 5*\/ 30 | / / 25 5*\/ 30 |
| / 8*3 / - -- + -------- / / 8*3 / - -- + -------- | | / / 8*3 / - -- + -------- / 8*3 / - -- + -------- | | / | 8*3 / - -- + -------- | / 8*3 / - -- + -------- | | / | 8*3 / - -- + -------- | / 8*3 / - -- + -------- |
| 1 \/ \/ 64 64 \/ \/ \/ 64 64 | |1 \/ \/ \/ 64 64 \/ \/ 64 64 | |1 \/ | \/ 64 64 | \/ \/ 64 64 | |1 \/ | \/ 64 64 | \/ \/ 64 64 |
-|- - + ------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------|*|- + ------------------------------------------------------------------------------------------------------------------------------------------------ - -------------------------------------------------------------------|*|- + --------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------|*|- + --------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------|
\ 4 2 2 / \4 2 2 / \4 2 2 / \4 2 2 /
$$- \left(- \frac{1}{4} + \frac{\sqrt{- \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + \frac{5}{2} + \frac{5}{4 \sqrt{- \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4}}}}}{2}\right) \left(- \frac{\sqrt{- \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4}}}{2} + \frac{1}{4} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + \frac{5}{2} + \frac{5}{4 \sqrt{- \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4}}}}}{2}\right) \left(\frac{\sqrt{\left|{- \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4}}\right|}}{2} + \frac{1}{4} - \frac{i \sqrt{- \frac{5}{2} - \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5 \left|{\frac{1}{\sqrt{- \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4}}}}\right|}{4}}}{2}\right) \left(\frac{\sqrt{\left|{- \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4}}\right|}}{2} + \frac{1}{4} + \frac{i \sqrt{- \frac{5}{2} - \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5 \left|{\frac{1}{\sqrt{- \frac{5}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}}} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{30}}{64}} + \frac{5}{4}}}}\right|}{4}}}{2}\right)$$
-(-1/4 + sqrt(5/4 + 2*(-25/64 + 5*sqrt(30)/64)^(1/3) - 5/(8*(-25/64 + 5*sqrt(30)/64)^(1/3)))/2 + sqrt(5/2 - 2*(-25/64 + 5*sqrt(30)/64)^(1/3) + 5/(4*sqrt(5/4 + 2*(-25/64 + 5*sqrt(30)/64)^(1/3) - 5/(8*(-25/64 + 5*sqrt(30)/64)^(1/3)))) + 5/(8*(-25/64 + 5*sqrt(30)/64)^(1/3)))/2)*(1/4 + sqrt(5/2 - 2*(-25/64 + 5*sqrt(30)/64)^(1/3) + 5/(4*sqrt(5/4 + 2*(-25/64 + 5*sqrt(30)/64)^(1/3) - 5/(8*(-25/64 + 5*sqrt(30)/64)^(1/3)))) + 5/(8*(-25/64 + 5*sqrt(30)/64)^(1/3)))/2 - sqrt(5/4 + 2*(-25/64 + 5*sqrt(30)/64)^(1/3) - 5/(8*(-25/64 + 5*sqrt(30)/64)^(1/3)))/2)*(1/4 + sqrt(Abs(5/4 + 2*(-25/64 + 5*sqrt(30)/64)^(1/3) - 5/(8*(-25/64 + 5*sqrt(30)/64)^(1/3))))/2 + i*sqrt(-5/2 + 2*(-25/64 + 5*sqrt(30)/64)^(1/3) - 5/(8*(-25/64 + 5*sqrt(30)/64)^(1/3)) + 5*Abs(1/sqrt(5/4 + 2*(-25/64 + 5*sqrt(30)/64)^(1/3) - 5/(8*(-25/64 + 5*sqrt(30)/64)^(1/3))))/4)/2)*(1/4 + sqrt(Abs(5/4 + 2*(-25/64 + 5*sqrt(30)/64)^(1/3) - 5/(8*(-25/64 + 5*sqrt(30)/64)^(1/3))))/2 - i*sqrt(-5/2 + 2*(-25/64 + 5*sqrt(30)/64)^(1/3) - 5/(8*(-25/64 + 5*sqrt(30)/64)^(1/3)) + 5*Abs(1/sqrt(5/4 + 2*(-25/64 + 5*sqrt(30)/64)^(1/3) - 5/(8*(-25/64 + 5*sqrt(30)/64)^(1/3))))/4)/2)
Numerical answer
[src]
x1 = -0.358716562180407 - 0.715222209696953*i
x2 = -0.358716562180407 + 0.715222209696953*i
x3 = 1.39589066665236
x4 = -1.67845754229154
x4 = -1.67845754229154