ta có :
(x+y+z)^2=x^2+y^2+z^2+2(xy+yz+xz)
⇒7^2=23+2(xy+yz+xz)
⇒xy+yz+xz=13
ta có : 6=7-1=x+y+z-1
⇒xy+z-6=xy+z-(x+y+z-1)=xy-y-x+1=y(x-1)-(x-1)=(x-1)(y-1)
⇒yz+x-6=yz+x-(x+y+z-1)=yz-y-z+1=y(z-1)-(z-1)=(y-1)(z-1)
⇒zx+y-6=zx+y-(x+y+z-1)=zx-x-z+1=x(z-1)-(z-1)=(z-1)(x-1)
ta có:
H=1/(xy+z-6)+1/(yz+x-6)+1/(zx+y-6)
H=1/(x-1)(y-1)+1/(y-1)(z-1)+1/(z-1)(x-1)
H=(z-1+x-1+y-1)/(x-1)(y-1)(z-1)
H=(x+y+z-3)/(xyz-xz-yz-xy+x+y+z-1) (phần mẫu là mik phân tích ra từ trên)
H=(7-3)/(3-13+7-1) (xz+yz+xy=13(cmt))
H=4/-4
⇒H=-1
nhớ cho mik 5 sao nha
H