Question : If $x-\frac{1}{x}=2$, then what is the value of $x^2+\frac{1}{x^2}$?
Option 1: 4
Option 2: 5
Option 3: 3
Option 4: 6
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Correct Answer: 6
Solution :
Given: $x-\frac{1}{x}=2$
We know that the algebraic identity is $(x-\frac{1}{x})^2=x^2+\frac{1}{x^2}-2$
$x-\frac{1}{x}=2$
On squaring both sides of the above equation, we get,
⇒ $(x-\frac{1}{x})^2=2^2$
⇒ $x^2+\frac{1}{x^2}-2=4$
⇒ $x^2+\frac{1}{x^2}=4+2$
⇒ $x^2+\frac{1}{x^2}=6$
Hence, the correct answer is 6.
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