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已知x,y满足x≥y≥1且2x2-xy-5x+y+4=0,则x+y的值( )A.有最小值5B.值为5C.值为4D.不能确
已知x,y满足x≥y≥1且2x2-xy-5x+y+4=0,则x+y的值()A.有最小值5B.值为5C.值为4D.不能确定...
已知x,y满足x≥y≥1且2x2-xy-5x+y+4=0,则x+y的值( )A.有最小值5B.值为5C.值为4D.不能确定
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∵2x2-5x+4=y(x-1),
∴2x2-xy-5x+y+4=0,
∵1≤y≤x,
∴x-1≥0,y≤x,
∴(x-1)y≤(x-1)x
则2x2-5x+4=(x-1)y≤(x-1)x,2x2-5x+4≤(x-1)x,即(x-2)2≤0,
∴x=2,
把x=2代入2x2-5x+4=y(x-1)得y=2.
∴x+y=4.
故选C.
∴2x2-xy-5x+y+4=0,
∵1≤y≤x,
∴x-1≥0,y≤x,
∴(x-1)y≤(x-1)x
则2x2-5x+4=(x-1)y≤(x-1)x,2x2-5x+4≤(x-1)x,即(x-2)2≤0,
∴x=2,
把x=2代入2x2-5x+4=y(x-1)得y=2.
∴x+y=4.
故选C.
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