Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation (x+6)^3=25*(x+6)
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Equation 1-5x=-6x+8
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Equation 1-5*x=-6*x+8
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Equation x^2-8*x+17=0
- Express {x} in terms of y where:
- -7*x-7*y=-14
- 10*x-2*y=0
- -15*x+17*y=13
- -11*x-15*y=14
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Identical expressions
- eighty *x^ six - eighty *x^ four + sixteen *x^ two = zero
- 80 multiply by x to the power of 6 minus 80 multiply by x to the power of 4 plus 16 multiply by x squared equally 0
- eighty multiply by x to the power of six minus eighty multiply by x to the power of four plus sixteen multiply by x to the power of two equally zero
- 80*x6-80*x4+16*x2=0
- 80*x⁶-80*x⁴+16*x²=0
- 80*x to the power of 6-80*x to the power of 4+16*x to the power of 2=0
- 80x^6-80x^4+16x^2=0
- 80x6-80x4+16x2=0
- 80*x^6-80*x^4+16*x^2=O
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Similar expressions
- 80*x^6-80*x^4-16*x^2=0
- 80*x^6+80*x^4+16*x^2=0
80*x^6-80*x^4+16*x^2=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Sum and product of roots
[src]
sum
___________ ___________ ___________ ___________
/ ___ / ___ / ___ / ___
/ 1 \/ 5 / 1 \/ 5 / 1 \/ 5 / 1 \/ 5
0 + 0 - / - - ----- + / - - ----- - / - + ----- + / - + -----
\/ 2 10 \/ 2 10 \/ 2 10 \/ 2 10
$$\left(- \sqrt{\frac{\sqrt{5}}{10} + \frac{1}{2}} + \left(\left(- \sqrt{\frac{1}{2} - \frac{\sqrt{5}}{10}} + \left(0 + 0\right)\right) + \sqrt{\frac{1}{2} - \frac{\sqrt{5}}{10}}\right)\right) + \sqrt{\frac{\sqrt{5}}{10} + \frac{1}{2}}$$
=
0
$$0$$
product
___________ ___________ ___________ ___________
/ ___ / ___ / ___ / ___
/ 1 \/ 5 / 1 \/ 5 / 1 \/ 5 / 1 \/ 5
1*0*- / - - ----- * / - - ----- *- / - + ----- * / - + -----
\/ 2 10 \/ 2 10 \/ 2 10 \/ 2 10
$$1 \cdot 0 \left(- \sqrt{\frac{1}{2} - \frac{\sqrt{5}}{10}}\right) \sqrt{\frac{1}{2} - \frac{\sqrt{5}}{10}} \left(- \sqrt{\frac{\sqrt{5}}{10} + \frac{1}{2}}\right) \sqrt{\frac{\sqrt{5}}{10} + \frac{1}{2}}$$
=
0
$$0$$
0
Rapid solution
[src]
x1 = 0
$$x_{1} = 0$$
___________
/ ___
/ 1 \/ 5
x2 = - / - - -----
\/ 2 10
$$x_{2} = - \sqrt{\frac{1}{2} - \frac{\sqrt{5}}{10}}$$
___________
/ ___
/ 1 \/ 5
x3 = / - - -----
\/ 2 10
$$x_{3} = \sqrt{\frac{1}{2} - \frac{\sqrt{5}}{10}}$$
___________
/ ___
/ 1 \/ 5
x4 = - / - + -----
\/ 2 10
$$x_{4} = - \sqrt{\frac{\sqrt{5}}{10} + \frac{1}{2}}$$
___________
/ ___
/ 1 \/ 5
x5 = / - + -----
\/ 2 10
$$x_{5} = \sqrt{\frac{\sqrt{5}}{10} + \frac{1}{2}}$$
Numerical answer
[src]
x1 = 0.85065080835204
x2 = -0.85065080835204
x3 = 0.0
x4 = -0.525731112119134
x5 = 0.525731112119134
x5 = 0.525731112119134
The graph