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 Notation

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

Solution steps

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

Refine

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

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

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

Solve

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

5 x^{4} + 15 x^{2} + 50 = 0

3 x^{3} - 3 x^{2} - 7 x + 5 = x^{3} - 2 x^{2} - 1

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

12 x^{2} + 48 x = - x^{3} - 64

0.75 = 10 x^{9} - 9 x^{10}

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))