Question

若X·Y满足3（X的平方+Y的平方+Z的平方）=（X=Y=Z)的平方.求证X+Y+Z

Answer 1

3（X^2+Y^2+Z^2）=（X+Y+Z)^2.求证X=Y=Z

3（X^2+Y^2+Z^2）=3X^2+3Y^2+3Z^2=（X+Y+Z)^2=X^2+Y^2+Z^2+2xy+2yz+2xz

整理：2x^2+2y^2+2z^2-2xy-2xz-2yz=o

(X^2+Y^2-2xy)+(x^2-2xz+Z^2)+(y^2-2yz+z^2)=0

(x-y)^2+(y-z)^2+(x-z)^2=0

x-y=0 y-z=0 x-z=0

x=y=z