Question

If a,b,c are all non-zero and a+b+c=0,Prove that a^2/bc+b^2/ac+c^2/ba =3

Answer 1

Step-by-step explanation:

by using formula

(a+b+c)(a^2+b^2+c^2-ab-bc-ca)=a^3+b^3+c^3-3abc

when a+b+c=0

(0)(a^2+b^2+c^2-ab-bc-ca)=a^3+b^3+c^3-3abc

0 =a^3+b^3+c^3-3abc

0+3abc= a^3+b^3+c^3

3abc=a^3+b^3+c^3

3= a^3+b^3+c^3/abc

3 =a^3/abc+b^3/abc+c^3/abc

3=a^2/bc+b^2/ac+c^2/ba

a^2/bc+b^2/ac+c^2/ba = 3