Question

Prove. 2(ab+bc+ca)>=a^2+b^2+c^2

Answer 1

We have to prove that,

    2 (ab + bc + ca) ≥ a² + b² + c²

Proof :

We know that,

(a + b + c)² = a² + b² + c² + 2 (ab + bc + ca)

⇒ 2 (ab + bc + ca) = (a + b + c)² - (a² + b² + c²)

⇒ 2 (ab + bc + ca) ≥ (a² + b² + c²)

Hence, proved.

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