If 2log(x + y)= logx + logy + log8 Prove that x²+y²= 6xy
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If 2log(x + y)= logx + logy + log8 Prove that x²+y²= 6xy
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Prove that x^2 + y^2 = 6xy :
LHS = 2log(x+ y)= logx+ logy+ log8
RHS = x^2 + y^2 = 6xy
x^2 + y^2 = 6xy
write the (x^2 + y^2 ) as (x+ y)^2−2xy;
(x+ y)^2−2xy = 6xy
(x+ y)^2 = 8xy
Taking log both sides;
= log(x+ y)2 = log(8xy)
= 2log(x+ y) = log8+logx + logy
= 2log(x+ y) = log2^3+logx+ logy
= 2log(x+ y)= 3log2+logx+ logy
= 2log(x+ y)= logx+ logy+ log8
∴ LHS = RHS
Hence proved.
Like for more information about the logarithmic calculations refer the link given below:
brainly.in/question/16912979