What are the solutions to the equation x^{16}+5x^8+4=0 ?

The solutions to the equation x^{16}+5x^8+4=0 are

Find the zeros of x^{16}+5x^8+4=0

The zeros of x^{16}+5x^8+4=0 are

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x^{16} + 5 x^{8} + 4 = 0

Solution steps

x^{16} + 5 x^{8} + 4 = 0

Rewrite the equation with

u = x^{2}, u^{4} = x^{8}

and

u^{8} = x^{16}

u^{8} + 5 u^{4} + 4 = 0

Solve

u^{8} + 5 u^{4} + 4 = 0 : u = \frac{1}{2} + \frac{1}{2} i, u = - \frac{1}{2} - \frac{1}{2} i, u = - \frac{1}{2} + \frac{1}{2} i, u = \frac{1}{2} - \frac{1}{2} i, u = 1 + i, u = - 1 - i, u = - 1 + i, u = 1 - i

u = \frac{1}{2} + \frac{1}{2} i, u = - \frac{1}{2} - \frac{1}{2} i, u = - \frac{1}{2} + \frac{1}{2} i, u = \frac{1}{2} - \frac{1}{2} i, u = 1 + i, u = - 1 - i, u = - 1 + i, u = 1 - i

Substitute back

u = x^{2},

solve for

x

Solve

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

Solve

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

Solve

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

Solve

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

The solutions are

x^{3} + 4 x^{2} + x - 6

x^{4} - 3 x^{3} - 13 x^{2} + 9 x + 30 = 0

7 y^{5} - 3 y^{1} = 2 y^{2}

10 x^{3} - 23 x - 1 = 0

a^{2} - 24 a n^{2} x^{2} + 144 n^{4} x^{4}

What are the solutions to the equation x^{16}+5x^8+4=0 ?
The solutions to the equation x^{16}+5x^8+4=0 are
Find the zeros of x^{16}+5x^8+4=0
The zeros of x^{16}+5x^8+4=0 are