Question

If a²+b²+c² =16, and ab + bc + ca=10, find the value of a+b+c.

Answer 1

Given : a² + b² + c² = 16 and ab + bc + ca = 10

We know that, (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 = 16 + 2(10)

(a + b + c)² = 16 + 20

(a + b + c)² = 36

(a + b + c)² = (±6)²

(a + b + c) = ±6

[Taking square root of both sides]

Hence, the value of a + b + c = ±6 .

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Answer 2

Answer:

Step-by-step explanation:

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

(a + b + c)² = 16 + 2(10)

(a + b + c)² = 16 + 20

(a + b + c)² = 36

(a + b + c)² = (±6)²

(a + b + c) = ±6