若（z-x)²－4（x-y)(y-z)=0,求2x+2z-4y的值

Question

若（z-x)²－4（x-y)(y-z)=0,求2x+2z-4y的值

Answer 1

（z-x)²－4（x-y)(y-z)
=[(x-y)+(y-z)]^2-4(x-y)(y-z)
=(x-y)^2+(y-z)^2+2(x-y)(y-z)-4(x-y)(y-z)
=(x-y)^2+(y-z)^2-2(x-y)(y-z)
=[(x-y)-(y-z)]^2
=(x+z-2y)^2
=0
x+z-2y=0
2x+2z-4y=2(x+z-2y)=2*0=0