Question : If the sum of $\frac{a}{b}$ and its reciprocal is 1 and $a\neq 0,b\neq 0$, then the value of $a^{3}+b^{3}$ is:
Option 1: 2
Option 2: –1
Option 3: 0
Option 4: 1
Answer (1)
12th Jan, 2024
Correct Answer: 0
Solution :
Given: $\frac{a}{b}$+$\frac{b}{a}= 1$
$⇒\frac{a^2+b^2}{ab}= 1$
$⇒a^2+b^2-ab= 0$---------(i)
Now, $a^{3}+b^{3}$
$=(a+b)(a^2+b^2-ab)$
$= (a+b)×0$
$=0$
Hence, the correct answer is 0.
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