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

Question

Question : If $x^{4} + \frac{1}{x^{4}} = 194, x > 0$ , then find the value of $x^{3} + \frac{1}{x^{3}} + x + \frac{1}{x}$
Option 1: 76
Option 2: 66
Option 3: 56
Option 4: 46

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Answer 1

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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Question : If x2+1x=5, then find the value of x4+1x4−36.Option 1: 491Option 2: 149Option 3: 419Option 4: 194

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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