What are the solutions to the equation x^8-17x^4+16=0 ?

The solutions to the equation x^8-17x^4+16=0 are x=2,x=-2,x=2i,x=-2i,x=1,x=-1,x=i,x=-i

Find the zeros of x^8-17x^4+16=0

The zeros of x^8-17x^4+16=0 are x=2,x=-2,x=2i,x=-2i,x=1,x=-1,x=i,x=-i

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x^{8} - 17 x^{4} + 16 = 0

x = 2, x = - 2, x = 2 i, x = - 2 i, x = 1, x = - 1, x = i, x = - i

Solution steps

x^{8} - 17 x^{4} + 16 = 0

Rewrite the equation with

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

and

u^{4} = x^{8}

u^{4} - 17 u^{2} + 16 = 0

Solve

u^{4} - 17 u^{2} + 16 = 0 : u = 4, u = - 4, u = 1, u = - 1

u = 4, u = - 4, u = 1, u = - 1

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = 4 : x = 2, x = - 2

Solve

x^{2} = - 4 : x = 2 i, x = - 2 i

Solve

x^{2} = 1 : x = 1, x = - 1

Solve

x^{2} = - 1 : x = i, x = - i

The solutions are

x = 2, x = - 2, x = 2 i, x = - 2 i, x = 1, x = - 1, x = i, x = - i

x^{3} + 8 i = 0

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

(x^{2} + x)^{2} - 18 (x^{2} + x) + 72 = 0

(w - 3) (w^{2} + 3 w + 9) = 2

x^{6} - 5 x^{4} + 6 x^{2} - 1 = 0

What are the solutions to the equation x^8-17x^4+16=0 ?
The solutions to the equation x^8-17x^4+16=0 are x=2,x=-2,x=2i,x=-2i,x=1,x=-1,x=i,x=-i
Find the zeros of x^8-17x^4+16=0
The zeros of x^8-17x^4+16=0 are x=2,x=-2,x=2i,x=-2i,x=1,x=-1,x=i,x=-i