Question

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

Answer 1

On expanding we get,
a^6+b^6+3a^4b^2+3a²b^4 = a^6+b^6+2a³b³
cancelling a^6 and b^6, we get
3a^4b^² + 3a²b^4 = 2a³b³
3a²b²(a² +b²) = 2ab (a²b²)
cancelling (a²b²),
a²+b²/ab = 2/3
⇒a²/ab + b²/ab =2/3
⇒a/b + b/a = 2/3

hope it helpss.... :)

Answer 2

Answer:

Value of $\frac{a}{b}+\frac{b}{a}\:\:is\:\:\frac{2}{3}$

Step-by-step explanation:

Given: ( a² + b² )³ = ( a³ + b³ )²

To find: Value of $\frac{a}{b}+\frac{b}{a}$

Consider,

( a² + b² )³ = ( a³ + b³ )²

$a^6+b^6+3a^2b^2(a^2+b^2)=a^6+b^6+2a^2b^2$

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

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

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

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

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

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

Therefore, value of $\frac{a}{b}+\frac{b}{a}\:\:is\:\:\frac{2}{3}$