What are the solutions to the equation 4x^3-3x= 1/2 ?

The solutions to the equation 4x^3-3x= 1/2 are x\approx-0.17364…,x\approx-0.76604…,x\approx 0.93969…

Find the zeros of 4x^3-3x= 1/2

The zeros of 4x^3-3x= 1/2 are x\approx-0.17364…,x\approx-0.76604…,x\approx 0.93969…

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4 x^{3} - 3 x = \frac{1}{2}

x \approx - 0.17364 \dots, x \approx - 0.76604 \dots, x \approx 0.93969 \dots

Solution steps

4 x^{3} - 3 x = \frac{1}{2}

Multiply both sides by

2

8 x^{3} - 6 x = 1

Move

1

to the left side

8 x^{3} - 6 x - 1 = 0

Find one solution for

8 x^{3} - 6 x - 1 = 0

using Newton-Raphson:

x \approx - 0.17364 \dots

Apply long division:

\frac{8 x ^{3} - 6 x - 1}{x + 0.17364 \dots} = 8 x^{2} - 1.38918 \dots x - 5.75877 \dots

8 x^{2} - 1.38918 \dots x - 5.75877 \dots \approx 0

Find one solution for

8 x^{2} - 1.38918 \dots x - 5.75877 \dots = 0

using Newton-Raphson:

x \approx - 0.76604 \dots

Apply long division:

\frac{8 x ^{2} - 1.38918 \dots x - 5.75877 \dots}{x + 0.76604 \dots} = 8 x - 7.51754 \dots

8 x - 7.51754 \dots \approx 0

x \approx 0.93969 \dots

The solutions are

x \approx - 0.17364 \dots, x \approx - 0.76604 \dots, x \approx 0.93969 \dots

x^{4} - 16 x^{2} + 16 = 0

(x + 1)^{4} + 1 = 0

35 = (1 + x)^{4}

234514 x^{3} - 746760 x + 395221 = 0

(r - 1)^{4} (r + 1) = 0

What are the solutions to the equation 4x^3-3x= 1/2 ?
The solutions to the equation 4x^3-3x= 1/2 are x\approx-0.17364…,x\approx-0.76604…,x\approx 0.93969…
Find the zeros of 4x^3-3x= 1/2
The zeros of 4x^3-3x= 1/2 are x\approx-0.17364…,x\approx-0.76604…,x\approx 0.93969…