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Question
If a + b + c = p and ab + bc + ca = q ; find a2 + b2 + c2.
Sum
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Solution
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
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Expansion of Formula
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