Question : If $\frac{x^2+1}{x}=5$, then find the value of $x^4+\frac{1}{x^4}-36$.
Option 1: 491
Option 2: 149
Option 3: 419
Option 4: 194
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Correct Answer: 491
Solution : $\frac{x^2+1}{x}=5$ ⇒ $x+\frac{1}{x}=5$ Squaring both sides, we get, ⇒ $x^2+\frac{1}{x^2}+2=25$ ⇒ $x^2+\frac{1}{x^2}=23$ Squaring both sides, we get, ⇒ $x^4+\frac{1}{x^4}+2=529$ Subtracting 38 from both sides. ⇒ $x^4+\frac{1}{x^4}-36 =491$ Hence, the correct answer is 491.
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