Mathematics
Find : a2 + b2 + c2, if a + b + c = 9 and ab + bc + ca = 24.
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Answer
Using the formula,
[∵ (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx]
So,
⇒ (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
⇒ (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
Putting (a + b + c) = 9 and (ab + bc + ca) = 24, we get
⇒ (9)2 = a2 + b2 + c2 + 2 x 24
⇒ 81 = a2 + b2 + c2 + 48
⇒ a2 + b2 + c2 = 81 - 48
⇒ a2 + b2 + c2 = 33
Hence, the value of a2 + b2 + c2 is 33.
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