Let x+y+z = 6...( 1)

The problem is transformed into x 2+y 2+z 2 =?

1/x+1/y+1/z = 0 universal integral (YZ+XZ+YZ)/XYZ=0.

That is yz+xz+yz = 0...(2)

(1) Both sides are squares:

X 2+y 2+z 2+2 (yz+xz+yz) = 36 in (2).

X 2+y 2+z 2 = 36。

So (A+ 1) 2+(B+2) 2+(C+3) 2 = 36.