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- Equation:
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Equation 0,6-1,6(x-4)=3(7-0,4x)
-
Equation 4^(x-1/2)-6*2^(x-1)+3=0
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Equation -x^2+8*x-12=0
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Equation 7x-(3+2x)=x+9
- Express {x} in terms of y where:
- -7*x-4*y=-5
- 2*x-9*y=-19
- 8*x+19*y=17
- 3*x-3*y=-14
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Identical expressions
- x^ four - five *x^ two - twelve *x+ forty-six = zero
- x to the power of 4 minus 5 multiply by x squared minus 12 multiply by x plus 46 equally 0
- x to the power of four minus five multiply by x to the power of two minus twelve multiply by x plus forty minus six equally zero
- x4-5*x2-12*x+46=0
- x⁴-5*x²-12*x+46=0
- x to the power of 4-5*x to the power of 2-12*x+46=0
- x^4-5x^2-12x+46=0
- x4-5x2-12x+46=0
- x^4-5*x^2-12*x+46=O
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Similar expressions
- x^4-5*x^2-12*x-46=0
- x^4-5*x^2+12*x+46=0
- x^4+5*x^2-12*x+46=0
x^4-5*x^2-12*x+46=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
4 2 x - 5*x - 12*x + 46 = 0
$$\left(- 12 x + \left(x^{4} - 5 x^{2}\right)\right) + 46 = 0$$
Sum and product of roots
[src]
sum
_____________________________________________________________________________________________________________________________________________________ _____________________________________________________________________________________________________________________________________________________ _____________________________________________________________________________________________________________________________________________________ _____________________________________________________________________________________________________________________________________________________
/ _____________________ / _____________________ / _____________________ / _____________________
/ / _______ / / _______ / / _______ / / _______
/ 20 / 10099 I*\/ 30902 24 577 / 20 24 / 10099 I*\/ 30902 577 / 20 / 10099 I*\/ 30902 24 577 / 20 24 / 10099 I*\/ 30902 577
I* / - -- + 2*3 / ----- + ----------- + ----------------------------------------------------------------------------- + ----------------------------- I* / - -- - ----------------------------------------------------------------------------- + 2*3 / ----- + ----------- + ----------------------------- I* / - -- + 2*3 / ----- + ----------- + ----------------------------------------------------------------------------- + ----------------------------- I* / - -- - ----------------------------------------------------------------------------- + 2*3 / ----- + ----------- + -----------------------------
___________________________________________________________________ / 3 \/ 216 4 ___________________________________________________________________ _____________________ ___________________________________________________________________ / 3 ___________________________________________________________________ \/ 216 4 _____________________ ___________________________________________________________________ / 3 \/ 216 4 ___________________________________________________________________ _____________________ ___________________________________________________________________ / 3 ___________________________________________________________________ \/ 216 4 _____________________
/ _____________________ / / _____________________ / _______ / _____________________ / / _____________________ / _______ / _____________________ / / _____________________ / _______ / _____________________ / / _____________________ / _______
/ / _______ / / / _______ / 10099 I*\/ 30902 / / _______ / / / _______ / 10099 I*\/ 30902 / / _______ / / / _______ / 10099 I*\/ 30902 / / _______ / / / _______ / 10099 I*\/ 30902
/ 10 / 10099 I*\/ 30902 577 / / 10 / 10099 I*\/ 30902 577 18*3 / ----- + ----------- / 10 / 10099 I*\/ 30902 577 / / 10 / 10099 I*\/ 30902 577 18*3 / ----- + ----------- / 10 / 10099 I*\/ 30902 577 / / 10 / 10099 I*\/ 30902 577 18*3 / ----- + ----------- / 10 / 10099 I*\/ 30902 577 / / 10 / 10099 I*\/ 30902 577 18*3 / ----- + -----------
/ -- + 2*3 / ----- + ----------- + ----------------------------- / / -- + 2*3 / ----- + ----------- + ----------------------------- \/ 216 4 / -- + 2*3 / ----- + ----------- + ----------------------------- / / -- + 2*3 / ----- + ----------- + ----------------------------- \/ 216 4 / -- + 2*3 / ----- + ----------- + ----------------------------- / / -- + 2*3 / ----- + ----------- + ----------------------------- \/ 216 4 / -- + 2*3 / ----- + ----------- + ----------------------------- / / -- + 2*3 / ----- + ----------- + ----------------------------- \/ 216 4
/ 3 \/ 216 4 _____________________ / / 3 \/ 216 4 _____________________ / 3 \/ 216 4 _____________________ / / 3 \/ 216 4 _____________________ / 3 \/ 216 4 _____________________ / / 3 \/ 216 4 _____________________ / 3 \/ 216 4 _____________________ / / 3 \/ 216 4 _____________________
/ / _______ / / / _______ / / _______ / / / _______ / / _______ / / / _______ / / _______ / / / _______
/ / 10099 I*\/ 30902 / / / 10099 I*\/ 30902 / / 10099 I*\/ 30902 / / / 10099 I*\/ 30902 / / 10099 I*\/ 30902 / / / 10099 I*\/ 30902 / / 10099 I*\/ 30902 / / / 10099 I*\/ 30902
/ 18*3 / ----- + ----------- / / 18*3 / ----- + ----------- / 18*3 / ----- + ----------- / / 18*3 / ----- + ----------- / 18*3 / ----- + ----------- / / 18*3 / ----- + ----------- / 18*3 / ----- + ----------- / / 18*3 / ----- + -----------
\/ \/ 216 4 \/ \/ \/ 216 4 \/ \/ 216 4 \/ \/ \/ 216 4 \/ \/ 216 4 \/ \/ \/ 216 4 \/ \/ 216 4 \/ \/ \/ 216 4
- ----------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- + - ----------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2 2 2 2 2 2 2
$$\left(\left(- \frac{i \sqrt{- \frac{20}{3} + \frac{577}{18 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}} + \frac{24}{\sqrt{\frac{10}{3} + \frac{577}{18 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}} + 2 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}}} + 2 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}}}{2} - \frac{\sqrt{\frac{10}{3} + \frac{577}{18 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}} + 2 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}}}{2}\right) + \left(\left(- \frac{i \sqrt{- \frac{20}{3} + \frac{577}{18 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}} - \frac{24}{\sqrt{\frac{10}{3} + \frac{577}{18 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}} + 2 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}}} + 2 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}}}{2} + \frac{\sqrt{\frac{10}{3} + \frac{577}{18 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}} + 2 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}}}{2}\right) + \left(- \frac{\sqrt{\frac{10}{3} + \frac{577}{18 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}} + 2 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}}}{2} + \frac{i \sqrt{- \frac{20}{3} + \frac{577}{18 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}} + \frac{24}{\sqrt{\frac{10}{3} + \frac{577}{18 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}} + 2 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}}} + 2 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}}}{2}\right)\right)\right) + \left(\frac{\sqrt{\frac{10}{3} + \frac{577}{18 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}} + 2 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}}}{2} + \frac{i \sqrt{- \frac{20}{3} + \frac{577}{18 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}} - \frac{24}{\sqrt{\frac{10}{3} + \frac{577}{18 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}} + 2 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}}} + 2 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}}}{2}\right)$$
=
0
$$0$$
product
/ _____________________________________________________________________________________________________________________________________________________\ / _____________________________________________________________________________________________________________________________________________________\ / _____________________________________________________________________________________________________________________________________________________\ / _____________________________________________________________________________________________________________________________________________________\ | / _____________________ | | / _____________________ | | / _____________________ | | / _____________________ | | / / _______ | | / / _______ | | / / _______ | | / / _______ | | / 20 / 10099 I*\/ 30902 24 577 | | / 20 24 / 10099 I*\/ 30902 577 | | / 20 / 10099 I*\/ 30902 24 577 | | / 20 24 / 10099 I*\/ 30902 577 | | I* / - -- + 2*3 / ----- + ----------- + ----------------------------------------------------------------------------- + ----------------------------- | | I* / - -- - ----------------------------------------------------------------------------- + 2*3 / ----- + ----------- + ----------------------------- | | I* / - -- + 2*3 / ----- + ----------- + ----------------------------------------------------------------------------- + ----------------------------- | | I* / - -- - ----------------------------------------------------------------------------- + 2*3 / ----- + ----------- + ----------------------------- | | ___________________________________________________________________ / 3 \/ 216 4 ___________________________________________________________________ _____________________ | | ___________________________________________________________________ / 3 ___________________________________________________________________ \/ 216 4 _____________________ | | ___________________________________________________________________ / 3 \/ 216 4 ___________________________________________________________________ _____________________ | | ___________________________________________________________________ / 3 ___________________________________________________________________ \/ 216 4 _____________________ | | / _____________________ / / _____________________ / _______ | | / _____________________ / / _____________________ / _______ | | / _____________________ / / _____________________ / _______ | | / _____________________ / / _____________________ / _______ | | / / _______ / / / _______ / 10099 I*\/ 30902 | | / / _______ / / / _______ / 10099 I*\/ 30902 | | / / _______ / / / _______ / 10099 I*\/ 30902 | | / / _______ / / / _______ / 10099 I*\/ 30902 | | / 10 / 10099 I*\/ 30902 577 / / 10 / 10099 I*\/ 30902 577 18*3 / ----- + ----------- | | / 10 / 10099 I*\/ 30902 577 / / 10 / 10099 I*\/ 30902 577 18*3 / ----- + ----------- | | / 10 / 10099 I*\/ 30902 577 / / 10 / 10099 I*\/ 30902 577 18*3 / ----- + ----------- | | / 10 / 10099 I*\/ 30902 577 / / 10 / 10099 I*\/ 30902 577 18*3 / ----- + ----------- | | / -- + 2*3 / ----- + ----------- + ----------------------------- / / -- + 2*3 / ----- + ----------- + ----------------------------- \/ 216 4 | | / -- + 2*3 / ----- + ----------- + ----------------------------- / / -- + 2*3 / ----- + ----------- + ----------------------------- \/ 216 4 | | / -- + 2*3 / ----- + ----------- + ----------------------------- / / -- + 2*3 / ----- + ----------- + ----------------------------- \/ 216 4 | | / -- + 2*3 / ----- + ----------- + ----------------------------- / / -- + 2*3 / ----- + ----------- + ----------------------------- \/ 216 4 | | / 3 \/ 216 4 _____________________ / / 3 \/ 216 4 _____________________ | | / 3 \/ 216 4 _____________________ / / 3 \/ 216 4 _____________________ | | / 3 \/ 216 4 _____________________ / / 3 \/ 216 4 _____________________ | | / 3 \/ 216 4 _____________________ / / 3 \/ 216 4 _____________________ | | / / _______ / / / _______ | | / / _______ / / / _______ | | / / _______ / / / _______ | | / / _______ / / / _______ | | / / 10099 I*\/ 30902 / / / 10099 I*\/ 30902 | | / / 10099 I*\/ 30902 / / / 10099 I*\/ 30902 | | / / 10099 I*\/ 30902 / / / 10099 I*\/ 30902 | | / / 10099 I*\/ 30902 / / / 10099 I*\/ 30902 | | / 18*3 / ----- + ----------- / / 18*3 / ----- + ----------- | | / 18*3 / ----- + ----------- / / 18*3 / ----- + ----------- | | / 18*3 / ----- + ----------- / / 18*3 / ----- + ----------- | | / 18*3 / ----- + ----------- / / 18*3 / ----- + ----------- | | \/ \/ 216 4 \/ \/ \/ 216 4 | |\/ \/ 216 4 \/ \/ \/ 216 4 | | \/ \/ 216 4 \/ \/ \/ 216 4 | |\/ \/ 216 4 \/ \/ \/ 216 4 | |- ----------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|----------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|- ----------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|----------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------| \ 2 2 / \ 2 2 / \ 2 2 / \ 2 2 /
$$\left(- \frac{i \sqrt{- \frac{20}{3} + \frac{577}{18 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}} - \frac{24}{\sqrt{\frac{10}{3} + \frac{577}{18 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}} + 2 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}}} + 2 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}}}{2} + \frac{\sqrt{\frac{10}{3} + \frac{577}{18 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}} + 2 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}}}{2}\right) \left(- \frac{\sqrt{\frac{10}{3} + \frac{577}{18 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}} + 2 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}}}{2} + \frac{i \sqrt{- \frac{20}{3} + \frac{577}{18 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}} + \frac{24}{\sqrt{\frac{10}{3} + \frac{577}{18 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}} + 2 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}}} + 2 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}}}{2}\right) \left(- \frac{i \sqrt{- \frac{20}{3} + \frac{577}{18 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}} + \frac{24}{\sqrt{\frac{10}{3} + \frac{577}{18 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}} + 2 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}}} + 2 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}}}{2} - \frac{\sqrt{\frac{10}{3} + \frac{577}{18 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}} + 2 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}}}{2}\right) \left(\frac{\sqrt{\frac{10}{3} + \frac{577}{18 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}} + 2 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}}}{2} + \frac{i \sqrt{- \frac{20}{3} + \frac{577}{18 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}} - \frac{24}{\sqrt{\frac{10}{3} + \frac{577}{18 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}} + 2 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}}} + 2 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}}}{2}\right)$$
=
46
$$46$$
46
Rapid solution
[src]
_____________________________________________________________________________________________________________________________________________________
/ _____________________
/ / _______
/ 20 / 10099 I*\/ 30902 24 577
I* / - -- + 2*3 / ----- + ----------- + ----------------------------------------------------------------------------- + -----------------------------
___________________________________________________________________ / 3 \/ 216 4 ___________________________________________________________________ _____________________
/ _____________________ / / _____________________ / _______
/ / _______ / / / _______ / 10099 I*\/ 30902
/ 10 / 10099 I*\/ 30902 577 / / 10 / 10099 I*\/ 30902 577 18*3 / ----- + -----------
/ -- + 2*3 / ----- + ----------- + ----------------------------- / / -- + 2*3 / ----- + ----------- + ----------------------------- \/ 216 4
/ 3 \/ 216 4 _____________________ / / 3 \/ 216 4 _____________________
/ / _______ / / / _______
/ / 10099 I*\/ 30902 / / / 10099 I*\/ 30902
/ 18*3 / ----- + ----------- / / 18*3 / ----- + -----------
\/ \/ 216 4 \/ \/ \/ 216 4
x1 = - ----------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2
$$x_{1} = - \frac{\sqrt{\frac{10}{3} + \frac{577}{18 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}} + 2 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}}}{2} + \frac{i \sqrt{- \frac{20}{3} + \frac{577}{18 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}} + \frac{24}{\sqrt{\frac{10}{3} + \frac{577}{18 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}} + 2 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}}} + 2 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}}}{2}$$
_____________________________________________________________________________________________________________________________________________________
/ _____________________
/ / _______
/ 20 24 / 10099 I*\/ 30902 577
I* / - -- - ----------------------------------------------------------------------------- + 2*3 / ----- + ----------- + -----------------------------
___________________________________________________________________ / 3 ___________________________________________________________________ \/ 216 4 _____________________
/ _____________________ / / _____________________ / _______
/ / _______ / / / _______ / 10099 I*\/ 30902
/ 10 / 10099 I*\/ 30902 577 / / 10 / 10099 I*\/ 30902 577 18*3 / ----- + -----------
/ -- + 2*3 / ----- + ----------- + ----------------------------- / / -- + 2*3 / ----- + ----------- + ----------------------------- \/ 216 4
/ 3 \/ 216 4 _____________________ / / 3 \/ 216 4 _____________________
/ / _______ / / / _______
/ / 10099 I*\/ 30902 / / / 10099 I*\/ 30902
/ 18*3 / ----- + ----------- / / 18*3 / ----- + -----------
\/ \/ 216 4 \/ \/ \/ 216 4
x2 = ----------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2
$$x_{2} = - \frac{i \sqrt{- \frac{20}{3} + \frac{577}{18 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}} - \frac{24}{\sqrt{\frac{10}{3} + \frac{577}{18 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}} + 2 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}}} + 2 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}}}{2} + \frac{\sqrt{\frac{10}{3} + \frac{577}{18 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}} + 2 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}}}{2}$$
_____________________________________________________________________________________________________________________________________________________
/ _____________________
/ / _______
/ 20 / 10099 I*\/ 30902 24 577
I* / - -- + 2*3 / ----- + ----------- + ----------------------------------------------------------------------------- + -----------------------------
___________________________________________________________________ / 3 \/ 216 4 ___________________________________________________________________ _____________________
/ _____________________ / / _____________________ / _______
/ / _______ / / / _______ / 10099 I*\/ 30902
/ 10 / 10099 I*\/ 30902 577 / / 10 / 10099 I*\/ 30902 577 18*3 / ----- + -----------
/ -- + 2*3 / ----- + ----------- + ----------------------------- / / -- + 2*3 / ----- + ----------- + ----------------------------- \/ 216 4
/ 3 \/ 216 4 _____________________ / / 3 \/ 216 4 _____________________
/ / _______ / / / _______
/ / 10099 I*\/ 30902 / / / 10099 I*\/ 30902
/ 18*3 / ----- + ----------- / / 18*3 / ----- + -----------
\/ \/ 216 4 \/ \/ \/ 216 4
x3 = - ----------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2
$$x_{3} = - \frac{i \sqrt{- \frac{20}{3} + \frac{577}{18 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}} + \frac{24}{\sqrt{\frac{10}{3} + \frac{577}{18 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}} + 2 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}}} + 2 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}}}{2} - \frac{\sqrt{\frac{10}{3} + \frac{577}{18 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}} + 2 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}}}{2}$$
_____________________________________________________________________________________________________________________________________________________
/ _____________________
/ / _______
/ 20 24 / 10099 I*\/ 30902 577
I* / - -- - ----------------------------------------------------------------------------- + 2*3 / ----- + ----------- + -----------------------------
___________________________________________________________________ / 3 ___________________________________________________________________ \/ 216 4 _____________________
/ _____________________ / / _____________________ / _______
/ / _______ / / / _______ / 10099 I*\/ 30902
/ 10 / 10099 I*\/ 30902 577 / / 10 / 10099 I*\/ 30902 577 18*3 / ----- + -----------
/ -- + 2*3 / ----- + ----------- + ----------------------------- / / -- + 2*3 / ----- + ----------- + ----------------------------- \/ 216 4
/ 3 \/ 216 4 _____________________ / / 3 \/ 216 4 _____________________
/ / _______ / / / _______
/ / 10099 I*\/ 30902 / / / 10099 I*\/ 30902
/ 18*3 / ----- + ----------- / / 18*3 / ----- + -----------
\/ \/ 216 4 \/ \/ \/ 216 4
x4 = ----------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2
$$x_{4} = \frac{\sqrt{\frac{10}{3} + \frac{577}{18 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}} + 2 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}}}{2} + \frac{i \sqrt{- \frac{20}{3} + \frac{577}{18 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}} - \frac{24}{\sqrt{\frac{10}{3} + \frac{577}{18 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}} + 2 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}}} + 2 \sqrt[3]{\frac{10099}{216} + \frac{\sqrt{30902} i}{4}}}}{2}$$
x4 = sqrt(10/3 + 577/(18*(10099/216 + sqrt(30902)*i/4)^(1/3)) + 2*(10099/216 + sqrt(30902)*i/4)^(1/3))/2 + i*sqrt(-20/3 + 577/(18*(10099/216 + sqrt(30902)*i/4)^(1/3)) - 24/sqrt(10/3 + 577/(18*(10099/216 + sqrt(30902)*i/4)^(1/3)) + 2*(10099/216 + sqrt(30902)*i/4)^(1/3)) + 2*(10099/216 + sqrt(30902)*i/4)^(1/3))/2
Numerical answer
[src]
x1 = 2.17045379174514 - 0.910313258851237*i
x2 = -2.17045379174514 + 1.89553926231068*i
x3 = -2.17045379174514 - 1.89553926231068*i
x4 = 2.17045379174514 + 0.910313258851237*i
x4 = 2.17045379174514 + 0.910313258851237*i