Question

if a + b + C is equal to 9 and a b + BC + C is equal to 40 find the value of a square + b square + c square

Answer 1

Given, a + b + c = 9 and ab + bc + ca = 40
We know that,
(a + b + c)2 = a 2 + b 2 + c 2 + 2ab + 2bc + 2ca
⇒ a 2 + b 2 + c 2 = (a + b + c)2 – 2 (ab + bc + ca)
⇒ a 2 + b 2 + c 2 = (9)2 – 2 × 40 = 81 – 80 = 1 [a + b + c = 9 and ab + bc + ca = 40]
Thus, the value of a 2 + b 2 + c2 is 1 .

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