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Let lgx + lgY = - 1. Find the minimum value of X + y, and find the value of X and y at this time
lgx+lgy=lg（x*y）=-1
x*y=1/10
According to the mean inequality
X times y when x + y is greater than or equal to 2 times the root sign
So the minimum value of X + y is 10
X = y = root 10 of 10
If x > 1, Y > 1 and lgx + lgY = 4, then the maximum value of lgxlgy is ()
A. 4B. 2C. 1D. 14
∵ x ＞ 1, y ＞ 1, ∵ lgx ＞ 0, lgY ＞ 0. ∵ lgx + lgY = 4 ≥ 2lgx · lgY, then lgxlgy ≤ 4, if and only if lgx = lgY = 2, take the equal sign. ∵ the maximum value of lgxlgy is 4
If x > 0, Y > 0 and X + y = 5, then the maximum value of lgx + lgY is 0______ ．
Because x ＞ 0, y ＞ 0 and X + y = 5, so x + y = 5 ≥ 2XY, the solution is XY ≤ 254, if and only if x = y = 52, take the equal sign, so lgx + lgY = LG (XY) ≤ lg254 = 2lg52, then the maximum value of lgx + lgY is 2lg52
If x > 0, Y > 0 and X + y = 5, then the maximum value of lgx + lgY is 0______ ．
Because x ＞ 0, y ＞ 0 and X + y = 5, so x + y = 5 ≥ 2XY, the solution is XY ≤ 254, if and only if x = y = 52, take the equal sign, so lgx + lgY = LG (XY) ≤ lg254 = 2lg52, then the maximum value of lgx + lgY is 2lg52
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