**If a**^{2} + b^{2} + c^{2} = 125 and ab + bc + ca = 50, find a + b + c.

^{2}+ b

^{2}+ c

^{2}= 125 and ab + bc + ca = 50, find a + b + c.

**Answer :**

We know that

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

Substituting the values

(a + b + c)^{2} = 125 + 2 (50)

By further calculation

(a + b + c)^{2} = 125 + 100 = 225

So we get

a + b + c = ± √225 = ± 15

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

By further calculation

ab + bc + ca = 44/2 = 22

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