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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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