Question

if log (x+y/4)=1/2 log x + 1/2 log y, show that x/y + y/x= 7

Answer 1

log(x+y/3)=logx^1/2+logy^1/2

log(x+y/3)=log(xy)^1/2

x+y/3=(xy)^1/2

square on both sides

x^2+y^2=9xy-2xy

x^2/xy+y^2/xy=7

x/y+y/x=7

therefore proved

i guess it helped