Question : If $a^{3} + \frac{1}{a^{3}} = 2$ , then the value of $\frac{a^{2} + 1}{a}$ is ( $a$ is a positive number):
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4

Question

Question : If $θ$ is a positive acute angle and $\tan 2 θ \tan 3 θ = 1$ , then the value of $2 (\cos^{2} \frac{5 θ}{2} - 1)$ is:
Option 1: $- \frac{1}{2}$
Option 2: -1
Option 3: 0
Option 4: $\frac{1}{2}$

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Answer 1

Correct Answer: 2

Solution : Given: $a^{3} + \frac{1}{a^{3}} = 2$
⇒ $a^{3} + \frac{1}{a^{3}} = 2$
⇒ $a^{6} + 1 = 2 a^{3}$
⇒ $a^{6} - 2 a^{3} + 1 = 0$
⇒ $(a^{3} - 1)^{2} = 0$
$a = 1$ , the above equation is satisfied.
Now putting $a = 1$ , in the equation, we get
$\frac{a^{2} + 1}{a} = \frac{1^{2} + 1}{1} = 2$
Hence, the correct answer is 2.

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Question : If a3+1a3=2, then the value of a2+1a is (a is a positive number):Option 1: 1Option 2: 2Option 3: 3Option 4: 4

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Question : If $a^{3} + \frac{1}{a^{3}} = 2$ , then the value of $\frac{a^{2} + 1}{a}$ is ( $a$ is a positive number):
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4