Question

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

Answer 1

We know that
( a + b + c )² = a² + b² + c² + 2( ab + bc + ca )    .....(1)
Given that, a + b + c = p and ab + bc + ca = q
We need to find a² + b² + c² :
Substitute the values of ( ab + bc + ca ) and ( a + b + c )
in the identity (1), we have
(p)² = a² + b² + c² + 2q
⇒ p² = a² + b² + c² + 2q
⇒ a² + b² + c² = p² - 2q