What are the solutions to the equation (2x^2-1)^2-8x^2+7=0 ?

The solutions to the equation (2x^2-1)^2-8x^2+7=0 are x=sqrt(2),x=-sqrt(2),x=1,x=-1

Find the zeros of (2x^2-1)^2-8x^2+7=0

The zeros of (2x^2-1)^2-8x^2+7=0 are x=sqrt(2),x=-sqrt(2),x=1,x=-1

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(2 x^{2} - 1)^{2} - 8 x^{2} + 7 = 0

x = 2, x = - 2, x = 1, x = - 1

Decimal Notation

x = 1.41421 \dots, x = - 1.41421 \dots, x = 1, x = - 1

Solution steps

(2 x^{2} - 1)^{2} - 8 x^{2} + 7 = 0

Expand

(2 x^{2} - 1)^{2} - 8 x^{2} + 7 : 4 x^{4} - 12 x^{2} + 8

4 x^{4} - 12 x^{2} + 8 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

4 u^{2} - 12 u + 8 = 0

Solve

4 u^{2} - 12 u + 8 = 0 : u = 2, u = 1

u = 2, u = 1

Substitute back

u = x^{2},

solve for

x

Solve

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

Solve

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

The solutions are

x = 2, x = - 2, x = 1, x = - 1

x^{4} - 2 x^{3} + 7 x + 9 = 0

x^{3} + 4 x^{2} - 3 x - 12 = 0

- 3 x^{4} + x^{3} - 187 x^{2} + 495 x + 414 = 0

x^{4} + 3 x^{3} - 6 x^{2} + 12 x - 40

125 x^{10} - 3 x^{7} = 0

What are the solutions to the equation (2x^2-1)^2-8x^2+7=0 ?
The solutions to the equation (2x^2-1)^2-8x^2+7=0 are x=sqrt(2),x=-sqrt(2),x=1,x=-1
Find the zeros of (2x^2-1)^2-8x^2+7=0
The zeros of (2x^2-1)^2-8x^2+7=0 are x=sqrt(2),x=-sqrt(2),x=1,x=-1