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Mathematics

Find: a + b + c, if a2 + b2 + c2 = 83 and ab + bc + ca = 71

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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 (a2 + b2 + c2) = 83 and (ab + bc + ca) = 71, we get

⇒ (a + b + c)2 = 83 + 2 x 71

⇒ (a + b + c)2 = 83 + 142

⇒ (a + b + c)2 = 225

⇒ a + b + c = 225\sqrt{225}

⇒ a + b + c = 15 or - 15

Hence, the values of (a + b + c) are 15 or - 15.

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