What are the solutions to the equation x^6-25x^4-16x^2+400=0 ?

The solutions to the equation x^6-25x^4-16x^2+400=0 are x=5,x=-5,x=2i,x=-2i,x=2,x=-2

Find the zeros of x^6-25x^4-16x^2+400=0

The zeros of x^6-25x^4-16x^2+400=0 are x=5,x=-5,x=2i,x=-2i,x=2,x=-2

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x^{6} - 25 x^{4} - 16 x^{2} + 400 = 0

x = 5, x = - 5, x = 2 i, x = - 2 i, x = 2, x = - 2

Solution steps

x^{6} - 25 x^{4} - 16 x^{2} + 400 = 0

Rewrite the equation with

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

and

u^{3} = x^{6}

u^{3} - 25 u^{2} - 16 u + 400 = 0

Solve

u^{3} - 25 u^{2} - 16 u + 400 = 0 : u = 25, u = - 4, u = 4

u = 25, u = - 4, u = 4

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = 25 : x = 5, x = - 5

Solve

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

Solve

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

The solutions are

x = 5, x = - 5, x = 2 i, x = - 2 i, x = 2, x = - 2

7 y^{3} + 17 y^{2} = 12 y

x, x^{3} + (y - 1)^{2} = 9

a, y = a^{3} + b^{2}

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

y^{4} + 12 y^{2} - 64 = 0

What are the solutions to the equation x^6-25x^4-16x^2+400=0 ?
The solutions to the equation x^6-25x^4-16x^2+400=0 are x=5,x=-5,x=2i,x=-2i,x=2,x=-2
Find the zeros of x^6-25x^4-16x^2+400=0
The zeros of x^6-25x^4-16x^2+400=0 are x=5,x=-5,x=2i,x=-2i,x=2,x=-2