Question : If $\frac{a}{b}+\frac{b}{a}=-1$ and $a-b=2$, then the value of $a^3-b^3$ is:
Option 1: $0$
Option 2: $\frac{1}{2}$
Option 3: $1$
Option 4: $–1$
Answer (1)
11th Jan, 2024
Correct Answer: $0$
Solution :
$\frac{a}{b}+\frac{b}{a}=-1$
⇒ $a^2 + b^2 + ab = 0$
Also, $a-b=2$
⇒ $a^3-b^3 = (a−b)(a^2+b^2+ab) = -2\times 0 = 0$
Hence, the correct answer is $0$.
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