Question

If a^3-b^3 = 0, then a/b+b/a=?

Answer 1

here is your answer mate

Answer 2

Method

First, let's find the solutions of the equation.

$a^3-b^3=0$

$\implies (a-b)(a^2+ab+b^2)=0$

Zero Product Rule

∴$a-b=0$ or $a^2+ab+b^2=0$

(I) $a-b=0$

$\dfrac{a}{b} +\dfrac{b}{a}$

$=\dfrac{a^2 + b^2}{ab}$

$=\dfrac{(a-b)^2+2ab}{ab}$

$=\dfrac{0+2ab}{ab} =2$

(II) $a^2+ab+b^2=0$

$\dfrac{a}{b} +\dfrac{b}{a}$

$=\dfrac{a^2 + b^2}{ab}$

$=\dfrac{(a^2+ab+b^2)-ab}{ab}$

$=\dfrac{0-ab}{ab} =-1$

Answer

Hence, the value of $\dfrac{a}{b} +\dfrac{b}{a} \:\:(a,b\neq 0)$ is 2 or -1.