What are the solutions to the equation x^4-x^2+1/8 =0 ?

The solutions to the equation x^4-x^2+1/8 =0 are

Find the zeros of x^4-x^2+1/8 =0

The zeros of x^4-x^2+1/8 =0 are

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x^{4} - x^{2} + \frac{1}{8} = 0

Decimal Notation

x = 0.92387 \dots, x = - 0.92387 \dots, x = 0.38268 \dots, x = - 0.38268 \dots

Solution steps

x^{4} - x^{2} + \frac{1}{8} = 0

Multiply both sides by

8

8 x^{4} - 8 x^{2} + 1 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

8 u^{2} - 8 u + 1 = 0

Solve

8 u^{2} - 8 u + 1 = 0 : u = \frac{2 + 2}{4}, u = \frac{2 - 2}{4}

u = \frac{2 + 2}{4}, u = \frac{2 - 2}{4}

Substitute back

u = x^{2},

solve for

x

Solve

The solutions are

x^{3} = 49 x

x^{4} + 29 x^{2} + 100 = 0

2 x^{3} + x^{2} - 13 x + 6 = 0

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

5 x^{4} - 10 x^{3} + 5 x^{2} = 0

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