Question : If the sum of a number and its reciprocal is 4, find the sum of their squares.
Option 1: 12
Option 2: 16
Option 3: 14
Option 4: 18
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Correct Answer: 14
Solution : Let the number be $x$. Reciprocal = $\frac{1}{x}$ According to the question, $x + \frac{1}{x} = 4$ Squaring both sides, we get: ⇒ $(x + \frac{1}{x})^2 = 4^2$ ⇒ $x^2+ \frac{1}{x^2}+2 = 16$ ⇒ $x^2 + \frac{1}{x^2} = 16 - 2 = 14$ Hence, the correct answer is 14.
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