Question

If a + b + c = 12 and a² + b² + c² = 50; find ab + bc + ca.

Answer 1

We know that
( a + b + c )² = a² + b² + c² + 2( ab + bc + ca )       .......(1)
Given that, a² + b² + c² = 50 and a + b + c = 12.
We need to find ab + bc + ca :
Substitute the values of  (a² + b² + c² ) and ( a + b + c )
in the identity (1), we have
(12)² = 50 + 2( ab + bc + ca )

⇒ 144 = 50 + 2( ab + bc + ca )
⇒ 94 = 2( ab + bc + ca)
⇒ ab + bc + ca = `94/2`
⇒ ab + bc + ca = 47