What are the solutions to the equation x^4+11x^2=3x^2+128 ?

The solutions to the equation x^4+11x^2=3x^2+128 are x=2sqrt(2),x=-2sqrt(2),x=4i,x=-4i

Find the zeros of x^4+11x^2=3x^2+128

The zeros of x^4+11x^2=3x^2+128 are x=2sqrt(2),x=-2sqrt(2),x=4i,x=-4i

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x^{4} + 11 x^{2} = 3 x^{2} + 128

x = 22, x = - 22, x = 4 i, x = - 4 i

Solution steps

x^{4} + 11 x^{2} = 3 x^{2} + 128

Move

128

to the left side

x^{4} + 11 x^{2} - 128 = 3 x^{2}

Move

3 x^{2}

to the left side

x^{4} + 8 x^{2} - 128 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

u^{2} + 8 u - 128 = 0

Solve

u^{2} + 8 u - 128 = 0 : u = 8, u = - 16

u = 8, u = - 16

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = 8 : x = 22, x = - 22

Solve

x^{2} = - 16 : x = 4 i, x = - 4 i

The solutions are

x = 22, x = - 22, x = 4 i, x = - 4 i

y^{4} - 7 y^{2} = - 10

5 x^{3} + 10 x^{2} + 5 x = 0

x^{3} + 10 = 0

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

4 x^{7} - 64 x^{3} = 0

What are the solutions to the equation x^4+11x^2=3x^2+128 ?
The solutions to the equation x^4+11x^2=3x^2+128 are x=2sqrt(2),x=-2sqrt(2),x=4i,x=-4i
Find the zeros of x^4+11x^2=3x^2+128
The zeros of x^4+11x^2=3x^2+128 are x=2sqrt(2),x=-2sqrt(2),x=4i,x=-4i