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Question -

If a + b + c = 9 and ab + bc + ca = 23, find the value of a2 + b2 + c2.



Answer -

(a + b + c)2 =a2 + b2 + c2 + 2(ab + bc + ca)
⇒ (9)2 = a2 + b2 +c2 + 2 x23
⇒ 81= a2 +b2 + c2 + 46
⇒  a2 + b2 +c2 = 81 – 46 = 35
∴ a2 + b2 + c2 =35

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