Question : If $a+\frac{1}{a}=5$, then what is the value of $a^3+\frac{1}{a^3} ?$
Option 1: 110
Option 2: 15
Option 3: 105
Option 4: –10
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Correct Answer: 110
Solution : Given, $a+\frac{1}{a}=5$ Cubing both sides, $(a+\frac{1}{a})^3=125$ ⇒ $a^3+\frac{1}{a^3}+3(a)(\frac{1}{a})(a+\frac{1}{a})=125$ ⇒ $a^3+\frac{1}{a^3}+3(1)(5)=125$ ⇒ $a^3+\frac{1}{a^3}=110$ Hence, the correct answer is 110.
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