Question

If x+y/7 =1/2 (log x + log y) then show x/y+y/x = 47
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Answer 1

Step-by-step explanation:

If log(x+y/7)=1/2(log x+log) then what is the proof of x/y+y/x=47?

log((x+y)/7)=1/2(logx+logy)

log((x+y)/7)=1/2(log(xy))

log((x+y)/7)=1/2(log(xy))

log((x+y)/7)=log(sqrt(xy))

(x+y)/7)=sqrt(xy)

Squaring on Both Sides,

(x+y)2=49xy

x2+y2+2xy=49xy

x2+y2=47xy

(x2+y2)/xy=47

x/y+y/x=47

Hence Proved!