若x＞0,y＞0,且2x+3y=6.则xy的最大值为＿＿＿＿.
由2x+3y=6,得y=2-(2/3)x；故xy=x[2-(2/3)x]=-(2/3)x²+2x=-(2/3)(x²-3x)=-(2/3)[(x-3/2)²-9/4]
=-(2/3)(x-3/2)²+3/2≦3/2
即当 x=3/2,y=1时xy获得最大值3/2.
若x＞0,y＞0,且2x+3x=6.则xy的最大值为＿＿＿＿.
若x＞0,y＞0,且2x+3y=6.则xy的最大值为＿＿＿＿.
由2x+3y=6,得y=2-(2/3)x；故xy=x[2-(2/3)x]=-(2/3)x²+2x=-(2/3)(x²-3x)=-(2/3)[(x-3/2)²-9/4]
=-(2/3)(x-3/2)²+3/2≦3/2
即当 x=3/2,y=1时xy获得最大值3/2.