Question

prove that(a+b+c)³ -a³ -b³ -c³ = 3(a+b)(b+c)(c+a)

Answer 1

Step-by-step explanation:

This is true only if a,b,c≥0

Apply AM≥GM for a,b

2a+b≥ab→ eqn 1

Apply AM≥GM for b,c

2b+c≥bc→ eqn 2

Apply AM≥GM for c,a

2c+a≥ca→ eqn 3

Multiply corresponding sides of eqn 1,2,3

⇒(a+b)(b+c)(c+a)≥8abc