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设正数x,y满足:x>y,x+2y=3,则1x-y+9x+5y的最小值为()A.83B.114C.4D.2
题目详情
设正数x,y满足:x>y,x+2y=3,则
+1 x-y
的最小值为( )9 x+5y
A. 8 3
B. 11 4
C. 4
D. 2
▼优质解答
答案和解析
正数x,y满足:x>y,x+2y=3,即有2x+4y=6,则1x-y+9x+5y=16[(x-y)+(x+5y)](1x-y+9x+5y)=16(10+x+5yx-y+9(x-y)x+5y)≥16(10+2x+5yx-y•9(x-y)x+5y)=16×16=83.当且仅当3(x-y)=x+5y,即有x=2,y=12,...
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