Question : If $x^2+\frac{1}{x^2}=4$, then what is the value of $x^4+\frac{1}{x^4}$?
Option 1: 16
Option 2: 14
Option 3: 12
Option 4: 20
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Correct Answer: 14
Solution :
Given that $x^2+\frac{1}{x^2}=4$,
Squaring both sides, we get,
$⇒(x^2+\frac{1}{x^2})^2 = 4^2$
$⇒x^4 + 2 + \frac{1}{x^4} = 16$
$⇒x^4 + \frac{1}{x^4} = 16 - 2 = 14$
Hence, the correct answer is 14.
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