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

The solutions to the equation x^6+4x^4-x^2-4=0 are x=2i,x=-2i,x=i,x=-i,x=1,x=-1

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

The zeros of x^6+4x^4-x^2-4=0 are x=2i,x=-2i,x=i,x=-i,x=1,x=-1

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

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

Solution steps

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

Rewrite the equation with

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

and

u^{3} = x^{6}

u^{3} + 4 u^{2} - u - 4 = 0

Solve

u^{3} + 4 u^{2} - u - 4 = 0 : u = - 4, u = - 1, u = 1

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

Substitute back

u = x^{2},

solve for

x

Solve

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

Solve

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

Solve

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

The solutions are

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

(x - 3)^{4} - 8 (x - 3)^{2} - 9 = 0

y, y^{2} = x^{3}

y, x^{3} + y^{3} = 1

x^{9} + x^{6} = 36

y, x^{4} + y^{4} = 16

What are the solutions to the equation x^6+4x^4-x^2-4=0 ?
The solutions to the equation x^6+4x^4-x^2-4=0 are x=2i,x=-2i,x=i,x=-i,x=1,x=-1
Find the zeros of x^6+4x^4-x^2-4=0
The zeros of x^6+4x^4-x^2-4=0 are x=2i,x=-2i,x=i,x=-i,x=1,x=-1