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

The solutions to the equation 2x^2=x^4+1 are x=1,x=-1

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

The zeros of 2x^2=x^4+1 are x=1,x=-1

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

x = 1, x = - 1

Solution steps

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

Switch sides

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

Move

2 x^{2}

to the left side

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

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

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

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

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

Solve

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

u = 1

Substitute back

u = x^{2},

solve for

x

Solve

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

The solutions are

x = 1, x = - 1

x^{4} = 25

(y^{2} - 3)^{2} - 9 (y^{2} - 3) - 52 = 0

4 x^{4} = 4000 x

x^{4} + 5 x^{2} = 36

x^{3} + 2 x^{2} = 9 x + 18

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