Question

abc不等于0,且a+b+c=0,则代数式(bc分之a)+(ca分之b)+(ab分之c)的值

Answer 1

原式= a 3 /abc+b 3 /abc+c 3 /abc =(a 3 +b 3 +c 3 )/abc =(a 3 +b 3 +c 3 -3abc)+3abc/abc (因为 a 3 +b 3 +c 3 -3abc=(a+b+c)(a 2 +b 2 +c 2 -ab-bc-ca)) =(a+b+c)(a 2 +b 2 +c 2 -ab-bc-ca)+3abc/abc (a+b+c=0) =3abc/abc =3