已知根号x根号下y-1根号下z-2=1已知根号下x+根号下y-1+根号下z-2=1/2(x+y+z),求xyz.

Question

已知根号x 根号下y-1 根号下z-2=1
已知根号下x+根号下y-1+根号下z-2=1/2(x+y+z),求xyz.

Answer 1

√x+√(y-1)+√(z-2)=(x+y+z)/2.
2√x+2√(y-1)+√2(z-2)-x-y-z=0
x+y+z-2√x-2√(y-1)-√2(z-2)=0
(x-2√x+1)+[(y-1)-2√(y-1)+1]+[(z-2)-2√(z-2)+1]=0.
(√x-1)²+[√(y-1)-1]²+[√(z-2)-1]²=0.
x-1=0,y-1=1,z-2=1
x=1,y=2,z=3.
xyz=6.