Question : If $a+\frac{1}{a}=5$, then determine the value of $a^3+\frac{1}{a^3}$.
Option 1: 90
Option 2: 125
Option 3: 105
Option 4: 110
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Answer (1)
24th Jan, 2024
Correct Answer: 110
Solution :
$a+\frac{1}{a}=5$
$⇒(a+\frac{1}{a})^3=5^3$
$⇒a^3+\frac{1}{a^3}+3×a×\frac{1}{a}(a+\frac{1}{a}) = 125$
$⇒a^3+\frac{1}{a^3} = 125 - (3×5) = 125 - 15 = 110$
Hence, the correct answer is 110.
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