Question

If $\frac{a}{b}+\frac{b}{a}=1$, then the value of $a^3+b^3$ is

• A. 1
• B. 0
• C. -1
• D. 2

Answer 1

The correct option is B 0

$\frac{a}{b}+\frac{b}{a}=1$

$\Rightarrow$ $\frac{a^2+b^2}{ab}=1$

$\Rightarrow$ $a^2+b^2=ab$ ----- ( 1 )

$\Rightarrow$ $a^3+b^3=(a+b)(a^2+b^2-ab)$

$=(a+b)(ab-ab)$ [ From ( 1 ) ]

$=(a+b)\left(0\right)$

$=0$

$\therefore$ $a^3+b^3=0$