实数x,y满足x≥y≥1和2x2-xy-5x+y+4=0,则x+y=______.
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/04/28 04:24:21
实数x,y满足x≥y≥1和2x2-xy-5x+y+4=0,则x+y=______.
∵2x2-xy-5x+y+4=0
∴x2+x2-xy-4x-x+y+4=0
∴x2-4x+4+x(x-y)-(x-y)=0
∴(x-2)2+(x-y)(x-1)=0
∵(x-2)2≥0,x≥y≥1,
∴(x-y)(x-1)≥0
因此两项都非负,只能都为0
∴x=y=2
∴x+y=4.
故答案为:4.
∴x2+x2-xy-4x-x+y+4=0
∴x2-4x+4+x(x-y)-(x-y)=0
∴(x-2)2+(x-y)(x-1)=0
∵(x-2)2≥0,x≥y≥1,
∴(x-y)(x-1)≥0
因此两项都非负,只能都为0
∴x=y=2
∴x+y=4.
故答案为:4.
实数x,y满足x≥y≥1和2x2-xy-5x+y+4=0,则x+y=______.
实数x、y满足x≥y≥1和2x^2-xy+5x-y+4=0,则x+y=___
实数x'y满足x≥y≥1和2x^2-xy-5x+y+4=0求x'y的值
实数x y满足x≥y≥1和2x²-xy-5x+y+4=0求x+y之值
已知实数x、y满足x2+4xy+4y2+x+2y-6=0,则x+2y的值为______.
已知正实数x,y满足xy+2x+y=4,则x+y的最小值为______.
已知实数x,y满足2x+y≥1,则u=x2+y2+4x-2y的最小值为______.
实数x、y满足x2+y2=4,则x+y-xy的最大值为______.
实数X,Y满足X大于等于Y大于等于1和2X平方-xy-5x+y+4=o,则x+y的值
已知实数x,y满足(x2)+(y2)-xy+2x-y+1=0,求x,y的值
已知实数x、y满足X2+y2-xy+2x-y+1=0,试求x、y的值
已知正实数x、y满足x+2y=xy,则2x+y的最小值等于______.