Question
1.
2.
3.
4.
Answer (Detailed Solution Below)
Option 4 : $322$
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Detailed Solution
सही उत्तर $322$ है।
Key Points
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prepsnap.in • Part -AQuestion:
If $x + \frac{1}{x} = 3$, then the value of $x^{6} + \frac{1}{x^{6}}$ is / यदि $x + \frac{1}{x} = 3$ है, तो $x^{6} + \frac{1}{x^{6}}$ का मान है
1.
$340$
2.
$300$
3.
$361$
4.
$322$
Correct Answer: $322$
$x^{2}+\frac{1}{x^{2}} = 3^{2}-2 = 7$; $x^{4}+\frac{1}{x^{4}} = 7^{2}-2 = 47$. Now $(x^{4}+\frac{1}{x^{4}})(x^{2}+\frac{1}{x^{2}}) = x^{6}+\frac{1}{x^{6}} + x^{2}+\frac{1}{x^{2}}$, so $x^{6}+\frac{1}{x^{6}} = 47\times7 - 7 = 322$. / चरणबद्ध: $7$, $47$, फिर $329-7=322$। Option (c) is the trap of squaring incorrectly: $(x^{3}+\frac{1}{x^{3}})^{2} = 18^{2}$ forgets the $-2$.
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