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

The solutions to the equation x^4-x^2+1/4 =0 are x= 1/(sqrt(2)),x=-1/(sqrt(2))

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

The zeros of x^4-x^2+1/4 =0 are x= 1/(sqrt(2)),x=-1/(sqrt(2))

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

x = \frac{1}{2}, x = - \frac{1}{2}

Decimal

x = 0.70710 \dots, x = - 0.70710 \dots

Solution steps

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

Multiply both sides by

4

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

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

4 u^{2} - 4 u + 1 = 0

Solve

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

u = \frac{1}{2}

Substitute back

u = x^{2},

solve for

x

Solve

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

The solutions are

x = \frac{1}{2}, x = - \frac{1}{2}

x^{3} - 12 x + 11 = 0

7 x^{3} - x^{2} - 7 x + 1

4 s^{3} + 15 s^{2} + 18 s + 5 = 0

x^{4} + 5 x^{2} = 6

2 x^{3} - 7 x^{2} - 5 x + 4 = 0

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