Question : If $x+\frac{1}{x}=7$, then the value of $x^2+\frac{1}{x^2}$ is:
Option 1: 49
Option 2: 51
Option 3: 47
Option 4: 5
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Correct Answer: 47
Solution :
Given, $x+\frac{1}{x}=7$
Squaring both sides, we get,
$⇒x^2+\frac{1}{x^2}+2×x×\frac{1}{x}=49$
$\therefore x^2+\frac{1}{x^2}=49-2=47$
Hence, the correct answer is 47.
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