Question

If (a3 + b3)2 = (a2 + b2)3 then find the value of a/b +b/a

Answer 1

Answer:

$\frac{2}{3}$

Step-by-step explanation:

Given,

$(a^3 + b^3)^2 = (a^2 + b^2)^3$

$(a^3)^2+2a^3b^3 + (b^3)^2 = (a^2)^3+3a^2b^2(a^2+b^2)+(b^2)^3$

$a^6+2a^3b^3+b^6=a^6+3a^2b^4+3a^4b^2+b^6$

$2a^3b^3=3a^2b^4+3a^4b^2$

$1=\frac{3a^2b^4}{2a^3b^3}+\frac{3a^4b^2}{2a^3b^3}$

$1=\frac{3b}{2a}+\frac{3a}{2b}$

$\frac{2}{3}=\frac{b}{a}+\frac{a}{b}$

Hence,

$\frac{b}{a}+\frac{a}{b}=\frac{2}{3}$

Answer 2

Answer:

The value of a/b +b/a = 2/3

Step-by-step explanation:

Given: $\left(a^{3}+b^{3}\right)^{2}=\left(a^{2}+b^{2}\right)^{3}$

Expanding it: $\left(a^{3}\right)^{2}+\left(b^{3}\right)^{2}+2 a^{3} b^{3}=\left(a^{2}\right)^{3}+\left(b^{2}\right)^{3}+3 a^{4} b+3 a^{2} b^{4}$

$\begin{array}{l}{a^{6}+b^{6}+2 a^{3} b^{3}=a^{6}+b^{6}+3 a^{4} b+3 a^{2} b^{4}} \\ {2 a^{3} b^{3}=3 a^{4} b^{2}+3 a^{2} b^{4}} \\ {2 a^{3} b^{3}-3 a^{4} b^{2}+3 a^{2} b^{4}=0}\end{array}$

$a^{3} b^{3}\left(2-3 b^{\frac{a}{b}}+3^{\frac{b}{a}}\right)=0$

a/b +b/a = 2/3