**If a + b + c = 12 and a**^{2} + b^{2} + c^{2} = 100, find ab + bc + ca.

^{2}+ b

^{2}+ c

^{2}= 100, find ab + bc + ca.

**Answer :**

We know that

**(a + b + c) ^{2} = a^{2} + b^{2} + c^{2} + 2ab + 2bc + 2ca**

It can be written as

2ab + 2bc + 2ca = (a + b + c)^{2} – (a^{2} + b^{2} + c^{2})

Taking out 2 as common

2 (ab + bc + ca) = 12^{2} – 100 = 144 – 100 = 44

By further calculation

ab + bc + ca = 44/2 = 22

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