What are the solutions to the equation (x^2-x)^2-(x^2-x)-12=0 ?

The solutions to the equation (x^2-x)^2-(x^2-x)-12=0 are x\approx 2.56155…,x\approx-1.56155…

Find the zeros of (x^2-x)^2-(x^2-x)-12=0

The zeros of (x^2-x)^2-(x^2-x)-12=0 are x\approx 2.56155…,x\approx-1.56155…

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(x^{2} - x)^{2} - (x^{2} - x) - 12 = 0

x \approx 2.56155 \dots, x \approx - 1.56155 \dots

Solution steps

(x^{2} - x)^{2} - (x^{2} - x) - 12 = 0

Expand

(x^{2} - x)^{2} - (x^{2} - x) - 12 : x^{4} - 2 x^{3} + x - 12

x^{4} - 2 x^{3} + x - 12 = 0

Find one solution for

x^{4} - 2 x^{3} + x - 12 = 0

using Newton-Raphson:

x \approx 2.56155 \dots

Apply long division:

\frac{x ^{4} - 2 x ^{3} + x - 12}{x - 2.56155 \dots} = x^{3} + 0.56155 \dots x^{2} + 1.43844 \dots x + 4.68465 \dots

x^{3} + 0.56155 \dots x^{2} + 1.43844 \dots x + 4.68465 \dots \approx 0

Find one solution for

x^{3} + 0.56155 \dots x^{2} + 1.43844 \dots x + 4.68465 \dots = 0

using Newton-Raphson:

x \approx - 1.56155 \dots

Apply long division:

\frac{x ^{3} + 0.56155 \dots x ^{2} + 1.43844 \dots x + 4.68465 \dots}{x + 1.56155 \dots} = x^{2} - x + 3.00000 \dots

x^{2} - x + 3.00000 \dots \approx 0

Find one solution for

x^{2} - x + 3.00000 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 2.56155 \dots, x \approx - 1.56155 \dots

x, y = x^{5}

x^{3} - 7 x^{2} + 5 x + 6 = 0

3 y^{4} - 5 y^{3} + 2 y^{2} = 0

x^{3} - 5 x^{2} - 7 x + 35 = 0

x^{5} + x^{2} = 1

What are the solutions to the equation (x^2-x)^2-(x^2-x)-12=0 ?
The solutions to the equation (x^2-x)^2-(x^2-x)-12=0 are x\approx 2.56155…,x\approx-1.56155…
Find the zeros of (x^2-x)^2-(x^2-x)-12=0
The zeros of (x^2-x)^2-(x^2-x)-12=0 are x\approx 2.56155…,x\approx-1.56155…