What is the answer to x^2=2-1/(x^2) ?

The answer to x^2=2-1/(x^2) is x=1,x=-1

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x^2=2-1/(x^2)

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

x = 1, x = - 1

Solution steps

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

Multiply both sides by

x^{2}

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

Solve

x^{4} = 2 x^{2} - 1 : x = 1, x = - 1

x = 1, x = - 1

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = 1, x = - 1

\frac{2}{x} = 1

\frac{1}{x} + \frac{1}{x - 1} = 0

x + 2 = \frac{15}{4 x + 1}

\frac{2}{u + 1} - \frac{u}{u - 1} = 3

y, x = \frac{2 y + 3}{y - 1}