Đáp án:
Ta có :
`x=a^2-bc⇒ax=a^3-abc; y=b^2-ac⇒by=b^3-abc; z=c^2-ab⇒cz=c^3-abc`
`⇒ax+by+cz=a^3+b^3+c^3−3abc`
Ta có :
`a^3+b^3+c^3−3abc=(a+b)^3+c^3−3ab(a+b)−3abc`
`=(a+b+c)(a^2+b^2+c^2+2ab−ac−bc)−3ab(a+b+c)`
`=(a+b+c)(a^2−bc+b^2−ac+c^2−ab)=(a+b+c)(x+y+z)`
Vậy : `(x+y+z)(a+b+c)=ax+by+cz` `\text{(đpcm)}`