Question

Choose the correct answer from the alternatives given.
If $(a^2+b^2{)}^3=(a^3+b^3{)}^2$, then $\frac{a}{b}+\frac{b}{a}$

• A. 1/3
• B. 2/3
• C. -1/3
• D. -2/3

Answer 1

The correct option is B 2/3

If $(a^2 + b^2)^3 = (a^3 + b^3 )^2$
$a^6 + b^6 + 3a^4b^2 + 3a^2b^4 = a^6 + b^6 + 2a^3b^3$
$3a^4b^2 + 3a^2b^4 = 2a^3b^3$
3(a^4b^2 + a^2b^4) = 2a^3b^3$
On dividing the equation by $a^3{b}^3$
$3\left(\frac{a^4{b}^2+a^2{b}^4}{a^3{b}^3}\right)=\frac{2a^3{b}^3}{a^3{b}^3}$
$(\frac{a}{b}+\frac{b}{a})=\frac{2}{3}$