If x
2
+ y
2
= 6xy then prove that 2log(x-y) = 2 log2 + log x+log y and 2log(x+y) = 3 log2 + log y
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1
Answer:
Given
x
2
+y
2
=25xy....(1)
L.H.S=2log(x+y)
=log(x+y)
2
=log(x
2
+y
2
+2xy)
=log(25xy+2xy) [ from (1)]
=log(27xy)
=log(3
3
xy)
=log3
3
+logx+logy
=3log3+logx+logy
=R.H.S
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