Question

if a + b + c = 0 Prove that a³-bc = b²-ac = c²- ab

Answer 1

Answer:

hello friend here is your answer

Step-by-step explanation:

we know that aCube+ bcube+c cube = a√3+b√3+c√3+2ab+2bc+2ca

so applying cube on both sides for equation

a√3+b√3+c√3

a√3+b√3+c√3+2ab+2bc+2ac

a√3+b√3+c√3+2(ab+bc+ca)

(a+b+c)√3+2(ab+ bc +ca)

we know a+b+c=0

0+2(ab+bc+ca)=0

2(ab+bc+ca )=0

applying cube on both sides

2(ab+bc+ca)√3=0√3

2ab √3+2bc√ 3+ 2ca√3=0

taking common ABC

2abc(b+c)