Question

If x² + y2 = 7xy then show than 2log
(×+y)=logx +logy+2log3​

Answer 1

Answer:

(take hint from 2log3 which is log 3^2 or log 9.....hmmm so I need 9 on RHS... but it is 7 only...no matter)

add 2xy both side we get

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

(x + y)^2 = 9xy

take log both side

log(x+y)^2 = log(9xy)

2log(x+y) = logx + logy + log9

2log(x+y) = logx + logy + 2log3 ( we already contemplated it earlier, so cut short one step here)