What are the solutions to the equation (x^2+1)^2=x ?

The solutions to the equation (x^2+1)^2=x are No Solution for x\in\mathbb{R}

Find the zeros of (x^2+1)^2=x

The zeros of (x^2+1)^2=x are No Solution for x\in\mathbb{R}

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(x^{2} + 1)^{2} = x

No Solution for x \in R

Solution steps

(x^{2} + 1)^{2} = x

Expand

(x^{2} + 1)^{2} : x^{4} + 2 x^{2} + 1

x^{4} + 2 x^{2} + 1 = x

Move

x

to the left side

x^{4} + 2 x^{2} + 1 - x = 0

Write in the standard form

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

x^{4} + 2 x^{2} - x + 1 = 0

Find one solution for

x^{4} + 2 x^{2} - x + 1 = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

No Solution for x \in R

(x^{2} + x) (x + 6 - x^{3}) = 5 x

x^{4} + x^{2} - 8 = 0

x^{3} - x = 4

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

(z + 2)^{3} = z^{2} + 5 z + 2

What are the solutions to the equation (x^2+1)^2=x ?
The solutions to the equation (x^2+1)^2=x are No Solution for x\in\mathbb{R}
Find the zeros of (x^2+1)^2=x
The zeros of (x^2+1)^2=x are No Solution for x\in\mathbb{R}