麻烦你们啦,再次深深鞠一躬!已知实数x,y,z满足x+y=5,z^2=xy+y-9,那么x+2y+3z=?我很着急

Question

麻烦你们啦,再次深深鞠一躬!已知实数x,y,z满足x+y=5,z^2=xy+y-9,那么x+2y+3z=?
我很着急

Answer 1

x=5-y
z2=(5-y)y+y-9
=6y-y2-9
=-(9-6y+y2)
=-(y-3)2
由题意,
只有当该项为0时等式成立
得y=3
那么
z=0 x=2
即
x+2y+3z
=2+6+0
=8