Question : If $\frac{x}{y}+\frac{y}{x}=1$ and $x+y=2$, then the value of $x^3+y^3$ is:
Option 1: 1
Option 2: 3
Option 3: 0
Option 4: 2
Answer (1)
24th Jan, 2024
Correct Answer: 0
Solution :
$\frac{x}{y}+\frac{y}{x}=1$ and $x+y=2$
$⇒\frac{x^2+y^2}{xy}=1$
$⇒{x^2+y^2}=xy$ ___(i)
$x^3+y^3=(x+y)(x^2+y^2-xy)$
From (i),
$⇒x^3+y^3=0$
Hence, the correct answer is 0.
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