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Mathematics

If (a + b + c) = 15 and (ab + bc + ca) = 74, find the value of (a2 + b2 + c2).

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Answer

Given,

(a + b + c) = 15

(ab + bc + ca) = 74

Using identity,

⇒ (a + b + c)2 = (a2 + b2 + c2) + 2 (ab + bc + ca)

⇒ (15)2 = (a2 + b2 + c2) + 2 (74)

⇒ 225 = (a2 + b2 + c2) + 148

⇒ 225 - 148 = (a2 + b2 + c2)

⇒ (a2 + b2 + c2) = 77

Hence, (a2 + b2 + c2) = 77.

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