Question : If $x^{2} - 3 x + 1 = 0$ , what is the value of $(x^{4} + \frac{1}{x^{4}})$ ?
Option 1: $11$
Option 2: $18$
Option 3: $47$
Option 4: $51$

Question

Question : If $x^{2} - 7 x + 1 = 0$ , what is the value of $(x + \frac{1}{x})$ .

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Answer 1

Correct Answer: $47$

Solution : Given: $x^{2} - 3 x + 1 = 0$
Divide both sides by $x$ , we get,
$\Rightarrow x - 3 + \frac{1}{x} = 0$
$∴ x + \frac{1}{x} = 3$
Squaring both sides, we get,
$\Rightarrow (x + \frac{1}{x})^{2} = 3^{2}$
$\Rightarrow x^{2} + \frac{1}{x^{2}} + 2 \times x \times \frac{1}{x} = 9$
$∴ x^{2} + \frac{1}{x^{2}} = 7$
Again squaring both sides, we get,
$\Rightarrow (x^{2} + \frac{1}{x^{2}})^{2} = 7^{2}$
$\Rightarrow x^{4} + \frac{1}{x^{4}} + 2 \times x^{2} \times \frac{1}{x^{2}} = 49$
$\Rightarrow (x^{4} + \frac{1}{x^{4}}) = 49 - 2$
$∴ (x^{4} + \frac{1}{x^{4}}) = 47$
Hence, the correct answer is $47$ .

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Question : If x2−3x+1=0, what is the value of (x4+1x4)?Option 1: 11Option 2: 18Option 3: 47Option 4: 51

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Question : If $x^{2} - 3 x + 1 = 0$ , what is the value of $(x^{4} + \frac{1}{x^{4}})$ ?
Option 1: $11$
Option 2: $18$
Option 3: $47$
Option 4: $51$