Question

If a² + b² + c² = 250 and ab + bc + ca = 3, find a + b + c.

Answer 1

Given : a² + b² + c² = 250 and ab + bc + ca = 3

To find : a + b + c

By using an identity, (a + b + c)² = a² + b² + c² + 2ab + 2 bc + 2 ca) :  

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

(a + b + c)² = 250 + 2(3)

(a + b + c)² = 250 + 6

(a + b + c)² = 256

(a + b + c)² = (±16)²

(a + b + c) = ±16

[Taking square root of both sides]

Hence, the value of a + b + c is  ±16 .

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