What are the solutions to the equation x^3=9x-1 ?

The solutions to the equation x^3=9x-1 are x\approx 0.11126…,x\approx 2.94282…,x\approx-3.05408…

Find the zeros of x^3=9x-1

The zeros of x^3=9x-1 are x\approx 0.11126…,x\approx 2.94282…,x\approx-3.05408…

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x^{3} = 9 x - 1

x \approx 0.11126 \dots, x \approx 2.94282 \dots, x \approx - 3.05408 \dots

Solution steps

x^{3} = 9 x - 1

Move

1

to the left side

x^{3} + 1 = 9 x

Move

9 x

to the left side

x^{3} + 1 - 9 x = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

x^{3} - 9 x + 1 = 0

Find one solution for

x^{3} - 9 x + 1 = 0

using Newton-Raphson:

x \approx 0.11126 \dots

Apply long division:

\frac{x ^{3} - 9 x + 1}{x - 0.11126 \dots} = x^{2} + 0.11126 \dots x - 8.98762 \dots

x^{2} + 0.11126 \dots x - 8.98762 \dots \approx 0

Find one solution for

x^{2} + 0.11126 \dots x - 8.98762 \dots = 0

using Newton-Raphson:

x \approx 2.94282 \dots

Apply long division:

\frac{x ^{2} + 0.11126 \dots x - 8.98762 \dots}{x - 2.94282 \dots} = x + 3.05408 \dots

x + 3.05408 \dots \approx 0

x \approx - 3.05408 \dots

The solutions are

x \approx 0.11126 \dots, x \approx 2.94282 \dots, x \approx - 3.05408 \dots

- 4 x^{4} + 4 = 0

x^{3} - 2.2 x^{2} - 6.61 x + 8.602 = 0

9 m^{5} - 27 m^{3} = 0

x^{4} - 4 x^{3} - 6 x^{2} + 4 x + 5 = 0

3 x^{4} + 17 x^{2} - 6 = 0

What are the solutions to the equation x^3=9x-1 ?
The solutions to the equation x^3=9x-1 are x\approx 0.11126…,x\approx 2.94282…,x\approx-3.05408…
Find the zeros of x^3=9x-1
The zeros of x^3=9x-1 are x\approx 0.11126…,x\approx 2.94282…,x\approx-3.05408…