If a + b + c = 12 and a2 + b2 + c2 = 100, find ab + bc + ca.

If a + b + c = 12 and a² + b² + c² = 100, find ab + bc + ca.

Answer :

We know that

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

It can be written as

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

Taking out 2 as common

2 (ab + bc + ca) = 12² – 100 = 144 – 100 = 44

By further calculation

ab + bc + ca = 44/2 = 22

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