Suppose-a-3-b-3-c-3-a-2-b-2-c-2-a-b-c-Prove-that-abc-0-

Question Number 176448 by peter frank last updated on 19/Sep/22

Suppose a^{3} + b^{3} + c^{3} = a^{2} + b^{2} + c^{2}

= a + b + c Prove that abc = 0

Commented by mr W last updated on 19/Sep/22

y o u {c a n}^{'} t p r o v e! b e c a u s e {i t}^{'} s n o t t r u e .

e x a m p l e a = b = c = 1 .

Commented by mr W last updated on 19/Sep/22

s u p p o s e

a^{3} + b^{3} + c^{3} = a^{2} + b^{2} + c^{2} = a + b + c = k

w e c a n g e t

a b c = \frac{k (k - 1) (k - 2)}{6} .

Commented by peter frank last updated on 19/Sep/22

thank you for clarification