Question : If $\frac{1}{x}+x=4$, then find $\frac{1}{x^2}+x^2$.
Option 1: 14
Option 2: 5
Option 3: 7
Option 4: 15
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Correct Answer: 14
Solution : $\frac{1}{x}+x=4$ squaring both sides we get, ⇒ $(\frac{1}{x}+x)^2=4^2$ ⇒ $\frac{1}{x^2}+2×\frac{1}{x}×x+x^2=16$ ⇒ $\frac{1}{x^2}+x^2=16-2$ ⇒ $\frac{1}{x^2}+x^2=14$ Hence, the correct answer is 14.
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