40X+90Y+20XY

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40X+90Y+20XY

40X+90Y+20XY
40X+90Y+20XY

40X+90Y+20XY
不妨设xy≥0,
40x+90y+20xy≤3200
0≥4x+9y+2xy-320≥12√(xy)+2xy-320
=2xy+12√(xy)-320
=2{[√(xy)]^2+6√(xy)+9}-338
=2[√(xy)+3]^2-338
2[√(xy)+3]^2-338≤0
[√(xy)+3]^2-169≤0
-13≤√(xy)+3≤13
-16≤√(xy)≤10
0≤√(xy)≤10
xy≤100

用基本不等式.再解不等式

楼上用均值不等式解题,应注意x大于零,y大于零