Question

已知(y-z)的平方+(x-y)的平方=2(y-z)(x-y),试说明x+z=2y

Answer 1

完全平方公式：a²-2ab+b²=(a-b)²

(y-z)²+(x-y)²=2(y-z)(x-y)

(y-z)²-2(y-z)(x-y)+(x-y)²=0

[(y-z)-(x-y)]²=0

(y-z)-(x-y)=0

y-z-x+y=0

x+z=2y