If a2 + b2 + c2 = 125 and ab + bc + ca = 50, find a + b + c.

If a² + b² + c² = 125 and ab + bc + ca = 50, find a + b + c.

Answer :

We know that

(a + b + c)² = a² + b² + c² + 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) = 12² – 100 = 144 – 100 = 44

By further calculation

ab + bc + ca = 44/2 = 22

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