Question : If $x^2-4 x-1=0$, then find the value of $x^2+\frac{1}{x^2}-5$.
Option 1: 17
Option 2: 12
Option 3: 15
Option 4: 13
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Correct Answer: 13
Solution : $x^2-4 x-1=0$ $x-\frac{1}{x} = 4$ Squaring on both sides, $ x^{2} + \frac{1}{x^{2}} - 2×x×\frac{1}{x} = 16$ $ x^{2} + \frac{1}{x^{2}} = 16+2 = 18$ -----------(i) Now, $x^2+\frac{1}{x^2}-5$ = 18 – 5 = 13 Hence, the correct answer is 13.
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