What are the solutions to the equation x^6-81x^2=0 ?

The solutions to the equation x^6-81x^2=0 are x=0,x=3i,x=-3i,x=3,x=-3

Find the zeros of x^6-81x^2=0

The zeros of x^6-81x^2=0 are x=0,x=3i,x=-3i,x=3,x=-3

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x^{6} - 81 x^{2} = 0

x = 0, x = 3 i, x = - 3 i, x = 3, x = - 3

Solution steps

x^{6} - 81 x^{2} = 0

Rewrite the equation with

u = x^{2}

and

u^{3} = x^{6}

u^{3} - 81 u = 0

Solve

u^{3} - 81 u = 0 : u = 0, u = - 9, u = 9

u = 0, u = - 9, u = 9

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = 0 : x = 0

Solve

x^{2} = - 9 : x = 3 i, x = - 3 i

Solve

x^{2} = 9 : x = 3, x = - 3

The solutions are

x = 0, x = 3 i, x = - 3 i, x = 3, x = - 3

4 x^{3} - 9 x^{2} + 6 x = 0

2 x^{3} + 10 x^{2} + 12 x = 0

x^{4} - 4 x^{3} - 5 x^{2} + 16 x + 4 = 0

x, (x^{2} + y^{2})^{2} = 4 x^{2} y

x, x^{3} = 7 x

What are the solutions to the equation x^6-81x^2=0 ?
The solutions to the equation x^6-81x^2=0 are x=0,x=3i,x=-3i,x=3,x=-3
Find the zeros of x^6-81x^2=0
The zeros of x^6-81x^2=0 are x=0,x=3i,x=-3i,x=3,x=-3