Question : If $\frac{a}{b}+\frac{b}{a}=1$, then the value of $(a^3+b^3)$ is:
Option 1: 1
Option 2: 0
Option 3: –1
Option 4: 2
Answer (1)
17th Jan, 2024
Correct Answer: 0
Solution :
Given: $\frac{a}{b}+\frac{b}{a}=1$
⇒ $\frac{a^2+b^2}{ab}=1$
⇒ $a^2+b^2=ab$
Now, $(a^3+b^3)=(a+b)(a^2+b^2-ab)$
Substitute the value of $a^2+b^2=ab$ in the above equation, we get,
$(a^3+b^3)=(a+b)(ab-ab)$
⇒ $(a^3+b^3)=(a+b)\times0$
⇒ $(a^3+b^3)=0$
Hence, the correct answer is 0.
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