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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