Question

log((x+y)/3)=1/2(log x+log y), then find the value of x/y + y/x​

Answer 1

Answer:

The value of  x/y + y/x = 7

Step-by-step explanation:

Given, log(( x + y)/3) = 1/2 (log x + log y)

         ⇒ log (( x + y)/3) = 1/2 log (x . y)

         ⇒  log (( x + y)/3) = log $\sqrt{(x . y)}$

         ⇒ (x + y)/ 3 =  $\sqrt{(x . y)}$

         ⇒ $(x+y)^2$ = 9 x .y

         ⇒ $x^{2}$ + $y^2$ + 2x .y = 9 x .y

         ⇒ $x^{2}$ + $y^2$ = 7 x .y

         ⇒ x/y + y/x = 7