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