Question

Factorise (b+c-a)(c+a-b)(a+b-c)+8abc​

Answer 1

Answer:

(a+b)(b+c)(c+a)≥8abc

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