已知实数x,y,z满足x+y=5,z^2=xy+y-9,那么x+2y+3z=?
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已知实数x,y,z满足x+y=5,z^2=xy+y-9,那么x+2y+3z=?已知实数x,y,z满足x+y=5,z^2=xy+y-9,那么x+2y+3z=?已知实数x,y,z满足x+y=5,z^2=x
已知实数x,y,z满足x+y=5,z^2=xy+y-9,那么x+2y+3z=?
已知实数x,y,z满足x+y=5,z^2=xy+y-9,那么x+2y+3z=?
已知实数x,y,z满足x+y=5,z^2=xy+y-9,那么x+2y+3z=?
∵x+y=5
∴y=5-x
∵z^2=xy+y-9
∴z^2=x(5-x)+(5-x)-9=-x^2+4x-4=-(x-2)^2
∴(x-2)^2+z^2=0
∵(x-2)^2≥0,z^2≥0
∴x-2=0,z=0
∴x=2,z=0,y=3
∴x+2y+3z=2+6+0=8.
z^2=xy+y+y^2-y^2-9
=y(x+y)+y-y^2-9
=5y+y-y^2-9
=-(y^2-6y+9)
=-(y-3)^2
∴z^2+(y-3)^2=0
由平方数的非负性得z=y-3=0
∴z=0,y=3
∴x=2
∴x+2y+3z=8
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