Question : If $x^{2} - 4 x + 1 = 0$ , then the value of $\frac{x^{6} + 1}{x^{3}}$ is:
Option 1: 48
Option 2: 52
Option 3: 55
Option 4: 58

Question

Question : If $(4 x + \frac{1}{x}) = 5, x \neq 0,$ then the value of $\frac{5 x}{4 x^{2} + 10 x + 1}$ is:

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Answer 1

Correct Answer: 52

Solution : Given:
$x^{2} - 4 x + 1 = 0$
Dividing both sides by $x$ we get,
⇒ $x - 4 + \frac{1}{x} = 0$
⇒ $x + \frac{1}{x} = 4$
⇒ $(x + \frac{1}{x})^{3} = 4^{3}$
⇒ $x^{3} + \frac{1}{x^{3}} + 3 \times x \times \frac{1}{x} \times (x + \frac{1}{x}) = 64$
⇒ $x^{3} + \frac{1}{x^{3}} + 3 \times 4 = 64$ [as, $x + \frac{1}{x} = 4$ ]
⇒ $x^{3} + \frac{1}{x^{3}} = 64 - 12$
$∴ \frac{x^{6} + 1}{x^{3}} = 52$
Hence, the correct answer is 52.

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Question : If x2−4x+1=0, then the value of x6+1x3 is:Option 1: 48Option 2: 52Option 3: 55Option 4: 58

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Question : If $x^{2} - 4 x + 1 = 0$ , then the value of $\frac{x^{6} + 1}{x^{3}}$ is:
Option 1: 48
Option 2: 52
Option 3: 55
Option 4: 58