Question

if $(a^2+b^2{)}^3=(a^3+b^3{)}^2$ then $\frac{a}{b}+\frac{b}{a}=$

• A. $\frac{2}{3}$
• B. $\frac{3}{2}$`
• C. $\frac{5}{6}$
• D. $\frac{6}{5}$

Answer 1

The correct option is A $\frac{2}{3}$

$(a^2+b^2{)}^3=(a^3+b^3{)}^2$
$\Rightarrow a^6+b^6+3a^4{b}^2+3a^2{b}^4=a^6+b^6+2a^3{b}^3$
$\Rightarrow 3a^4{b}^2+3a^2{b}^4=2a^3{b}^3$
$\Rightarrow a^4{b}^2+a^2{b}^4=\frac{2}{3}{a}^3{b}^3$
$\Rightarrow \frac{a^4{b}^2+a^2{b}^4}{a^3{b}^3}=\frac{2}{3}$
$\Rightarrow \frac{a}{b}+\frac{b}{a}=\frac{2}{3}$
Option A is correct.