Question

已知x-y=6,xy=-8求代数式(x+y+z)²+1/2(x-y-z)(x-y+z)-z(x+y

已知x-y=6,xy=-8求代数式(x+y+z)²+1/2(x-y-z)(x-y+z)-z(x+y)的值

Answer 1

化简得： 1/2(x+y+z)方+1/2(x-y-z)(x-y+z)-z(x+y)= 1/2[(x+y)方+2z(x+y)+z方]+1/2[(x-y)方-z方]-z(x+y)= 1/2(x+y)方+1/2(x-y)方=x方＋y方 由x-y=6,xy=21得，x方＋y方＝（x-y）方＋2xy＝78