Question : If $x^2+\frac{1}{x^2}=29$, then find the value of $x-\frac{1}{x}$.
Option 1: $\pm 4$
Option 2: $\pm 3 \sqrt{3}$
Option 3: $\pm 3$
Option 4: $\pm 4 \sqrt{3}$
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Correct Answer: $\pm 3 \sqrt{3}$
Solution :
$x^2+\frac{1}{x^2}=29$
$⇒x^2+\frac{1}{x^2} - 2=29-2$
$⇒(x-\frac{1}{x})^2 = 27$
$⇒(x-\frac{1}{x})^2 = 27$
$⇒(x-\frac{1}{x}) = \pm \sqrt{27}$
$\therefore (x-\frac{1}{x}) = \pm 3\sqrt{3}$
Hence, the correct answer is $\pm 3\sqrt{3}$.
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