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If x > 0, Y > 0 and X + y = 5, the maximum value of lgx + lgY is (?)
According to the mean inequality
5=x+y≥2√xy
√xy≤5/2
xy≤(5/2)²
If and only if x = y = 5 / 2, the equal sign holds
therefore
lgx+lgy
=lgxy
≤lg(5/2)²
=2lg(5/2)
=2lg(10/4)
=2(lg10-lg4)
=2-2lg4
x> 0, Y > 0, and X + y = 5, then the maximum value of lgx + lgY
lgx+lgy=lg(xy)
x=5-y
xy=5y-y^2
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