Question

If a² + b² + c² = 35 and ab + bc + ca = 23; find a + b + c.

Answer 1

We know that
(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)   ...(1)
Given that, a² + b² + c² = 35 and ab + bc + ca = 23
We need to find a + b + c :
Substitute the values of (a² + b² + c²) and (ab + bc + ca)
in the identity (1), we have
(a + b + c)² = 35 + 2(23)
⇒ (a + b + c)² = 81
⇒ a + b + c = `+-sqrt81` 
⇒ a + b + c = `+-9`