If x ＞ 1, y ＞ 1, xy = 10, then the maximum value of lgx · lgY is 0______ ．

If x ＞ 1, y ＞ 1, xy = 10, then the maximum value of lgx · lgY is 0______ ．

∵ x ＞ 1, y ＞ 1, xy = 10, ∵ lgx ＞ 0, lgY ＞ 0, ∵ lgxlgy ≤ lgx + lgy2 = lgxy2 = lg102 = 12, if and only if lgx = lgY, i.e. x = y = 10, take the equal sign. The maximum value of ∵ lgx · lgY ≤ 14, ∵ lgx · lgY is 14

A high school math problem: if the two sides of the equation LG's Square x + (lg5 + lg7) lgx + lg5 · lg7 are a and B, what is the value of a · B? I use x1 · x2 = B / a directly, but it seems wrong. Thank you

The square x + (lg5 + lg7) lgx + lg5 · lg7 of LG
=（lgx+lg5）（lgx+lg7）
lgx=-lg5 a=1/5
lgx=-lg7 b=1/7
a*b=1/35
a-b=2/35

If two of the equations LG square x + (lg7 + lg5) * lgx + lg7 * lg5 = 0 are X1 and X2, then X1 * x2 =?

LG square x + (lg7 + lg5) * lgx + lg7 * lg5 = 0
(lgx+lg7)(lgx+lg5)=0
lgx+lg7=0,lgx=-lg7=lg(7)^-1=lg(1/7),x1=1/7,
lgx=-lg5,x2=1/5,
x1*x=1/7*1/5=1/35

Let f (x) = LG [(1 + 2 ^ x + A * 4 ^ x) / 2] where a ∈ R, if f (x) is meaningful when x (- ∞, 1], the value range of a is obtained

F (x) = LG [(1 + 2 ^ x + A * 4 ^ x) / 2], i.e. 1 + 2 ^ x + a · 4 ^ x > 0 → a > (- 1) / (4 ^ x) - 1 / (2 ^ x), let 1 / (2 ^ x) = y, i.e. a > - y ^ 2-y = - (y + 1 / 2) ^ 2 + 1 / 4, and X ∈ (- ∞, 1)] and f (x) is meaningful in this interval, so a > 1 / 4 is obtained from a > - y ^ 2-y = - (y + 1 / 2) ^ 2 + 1 / 4