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

The solutions to the equation x^3-3x=1 are x\approx-0.34729…,x\approx-1.53208…,x\approx 1.87938…

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

The zeros of x^3-3x=1 are x\approx-0.34729…,x\approx-1.53208…,x\approx 1.87938…

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x^{3} - 3 x = 1

x \approx - 0.34729 \dots, x \approx - 1.53208 \dots, x \approx 1.87938 \dots

Solution steps

x^{3} - 3 x = 1

Move

1

to the left side

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

Find one solution for

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

using Newton-Raphson:

x \approx - 0.34729 \dots

Apply long division:

\frac{x ^{3} - 3 x - 1}{x + 0.34729 \dots} = x^{2} - 0.34729 \dots x - 2.87938 \dots

x^{2} - 0.34729 \dots x - 2.87938 \dots \approx 0

Find one solution for

x^{2} - 0.34729 \dots x - 2.87938 \dots = 0

using Newton-Raphson:

x \approx - 1.53208 \dots

Apply long division:

\frac{x ^{2} - 0.34729 \dots x - 2.87938 \dots}{x + 1.53208 \dots} = x - 1.87938 \dots

x - 1.87938 \dots \approx 0

x \approx 1.87938 \dots

The solutions are

x \approx - 0.34729 \dots, x \approx - 1.53208 \dots, x \approx 1.87938 \dots

x^{2 + 1} = 8

v^{3} = 8

m^{3} - 64 = 0

3^{3} = (9 x^{3})

x^{3} - 3 x = x

What are the solutions to the equation x^3-3x=1 ?
The solutions to the equation x^3-3x=1 are x\approx-0.34729…,x\approx-1.53208…,x\approx 1.87938…
Find the zeros of x^3-3x=1
The zeros of x^3-3x=1 are x\approx-0.34729…,x\approx-1.53208…,x\approx 1.87938…