What are the solutions to the equation x^4-4x^2+5=0-1 ?

The solutions to the equation x^4-4x^2+5=0-1 are

Find the zeros of x^4-4x^2+5=0-1

The zeros of x^4-4x^2+5=0-1 are

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x^{4} - 4 x^{2} + 5 = 0 - 1

x = \frac{2 + 6}{2} + \frac{1}{2 + 6} i, x = - \frac{2 + 6}{2} - \frac{1}{2 + 6} i, x = \frac{2 + 6}{2} - \frac{1}{2 + 6} i, x = - \frac{2 + 6}{2} + \frac{1}{2 + 6} i

Solution steps

x^{4} - 4 x^{2} + 5 = 0 - 1

Refine

x^{4} - 4 x^{2} + 5 = - 1

Move

1

to the left side

x^{4} - 4 x^{2} + 6 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

u^{2} - 4 u + 6 = 0

Solve

u^{2} - 4 u + 6 = 0 : u = 2 + 2 i, u = 2 - 2 i

u = 2 + 2 i, u = 2 - 2 i

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = 2 + 2 i : x = \frac{2 + 6}{2} + \frac{1}{2 + 6} i, x = - \frac{2 + 6}{2} - \frac{1}{2 + 6} i

Solve

x^{2} = 2 - 2 i : x = \frac{2 + 6}{2} - \frac{1}{2 + 6} i, x = - \frac{2 + 6}{2} + \frac{1}{2 + 6} i

The solutions are

x = \frac{2 + 6}{2} + \frac{1}{2 + 6} i, x = - \frac{2 + 6}{2} - \frac{1}{2 + 6} i, x = \frac{2 + 6}{2} - \frac{1}{2 + 6} i, x = - \frac{2 + 6}{2} + \frac{1}{2 + 6} i

(x^{3} - 2) = - 25

0 = x^{3} - 4 x^{2} - 25 x + 100

x^{3} + 2 x^{2} - 10 x = 0

r^{3} + 2 r^{2} + r = 0

x^{3} - 45 x = 4 x^{2}

What are the solutions to the equation x^4-4x^2+5=0-1 ?
The solutions to the equation x^4-4x^2+5=0-1 are
Find the zeros of x^4-4x^2+5=0-1
The zeros of x^4-4x^2+5=0-1 are