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`