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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