What are the solutions to the equation (x^2-3x)^2-(x^2-3)^2-8=0 ?

The solutions to the equation (x^2-3x)^2-(x^2-3)^2-8=0 are x\approx-0.91135…

Find the zeros of (x^2-3x)^2-(x^2-3)^2-8=0

The zeros of (x^2-3x)^2-(x^2-3)^2-8=0 are x\approx-0.91135…

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(x^{2} - 3 x)^{2} - (x^{2} - 3)^{2} - 8 = 0

x \approx - 0.91135 \dots

Solution steps

(x^{2} - 3 x)^{2} - (x^{2} - 3)^{2} - 8 = 0

Expand

(x^{2} - 3 x)^{2} - (x^{2} - 3)^{2} - 8 : - 6 x^{3} + 15 x^{2} - 17

- 6 x^{3} + 15 x^{2} - 17 = 0

Find one solution for

- 6 x^{3} + 15 x^{2} - 17 = 0

using Newton-Raphson:

x \approx - 0.91135 \dots

Apply long division:

\frac{- 6 x ^{3} + 15 x ^{2} - 17}{x + 0.91135 \dots} = - 6 x^{2} + 20.46810 \dots x - 18.65362 \dots

- 6 x^{2} + 20.46810 \dots x - 18.65362 \dots \approx 0

Find one solution for

- 6 x^{2} + 20.46810 \dots x - 18.65362 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx - 0.91135 \dots

x^{2} (2 x + 3) = 35

(3 x - 2) (x + 1)^{2} (3 x + 8) = 16

x^{3} - x^{2} - 2 x = 0

(x^{2} + x) (x^{2} - x) = (x - 2)^{2} + x (x + 4)

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

What are the solutions to the equation (x^2-3x)^2-(x^2-3)^2-8=0 ?
The solutions to the equation (x^2-3x)^2-(x^2-3)^2-8=0 are x\approx-0.91135…
Find the zeros of (x^2-3x)^2-(x^2-3)^2-8=0
The zeros of (x^2-3x)^2-(x^2-3)^2-8=0 are x\approx-0.91135…