Can anyone please help me in doing the following question:
Given that x^2 + y^2 = 6xy, find an equivalent expression to 2 log(x+y).
Thanks any help will be greatly appreciated.
Given that x^2 + y^2 = 6xy, find an equivalent expression to 2 log(x+y).
2log(x+y)
= log[(x+y)^2]
= log[x^2 +2xy +y^2] ------------(i)
x^2 +y^2 = 6xy
Add 2xy to both sides,
x^2 +2xy +y^2 = 8xy
(x +y)^2 = 8xy
So,
2log(x+y)
= log(8xy) --------------answer.
Or,
= log(8) +log(x) +log(y)
= log(2^3) +log(x) +log(y)
= 3log(2) +log(x) +log(y) -------------answer also.