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

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

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

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

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

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

Decimal Notation

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

Solution steps

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

y, y^{4} = x

x^{3} - 3 x + 1

120 t^{2} - 15 t^{4} = 0

x^{5} - x^{4} - 10 x^{3} + 10 x^{2} - 11 x + 11 = 0

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