If x + (1/x) = 2 then x2 + (1/x2​) = ?

Answer: \(x^{2}+ \frac{1}{x^{2}} = 2\)

Given

\(x + \frac{1}{x}= 2\)

To find:

\(x^{2} + \frac{1}{x^{2}}\)

Squaring on both the side we get

\(\left (x + \frac{1}{x} \right)^{2}= 2^{2}\) \(\left (x + \frac{1}{x} \right)^{2}= 4\) \(x^{2}+ \frac{1}{x^{2}}+ 2\times x\times \frac{1}{x}= 4\) \(x^{2}+ \frac{1}{x^{2}}+ 2 = 4\) \(x^{2}+ \frac{1}{x^{2}} = 4 – 2\) \(x^{2}+ \frac{1}{x^{2}} = 2\)

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