设0﹤x﹤1,0﹤y﹤1,且(1-xy)=2(1-x)(1-y).则函数f(x,y)=1/2* xy(1-xy)的最大值.谢谢了,大神帮忙啊

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设0﹤x﹤1,0﹤y﹤1,且(1-xy)=2(1-x)(1-y).则函数f(x,y)=1/2* xy(1-xy)的最大值.谢谢了,大神帮忙啊

(1-xy)=2(1-x)(1-y) 1-2xy+x y=2(1-x-y+xy) 即:1+4xy-xy=2(x+y)≥4√(xy)等号仅当x=y取得.令xy=t,0﹤x﹤1,0﹤y﹤1,那么t ∈﹙0,1) 1+4t-t^4≥4t 即:t^4+4t-4t-1≤0,[(t+1)-2] (t-1) ≤0,因为 t ∈﹙0,1),...