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Mathematics

If (a + b + c) = 14 and (a2 + b2 + c2) = 74, find the value of (ab + bc + ca).

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Answer

Given,

(a + b + c) = 14

(a2 + b2 + c2) = 74

Using identity,

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

⇒ (14)2 = (74) + 2 (ab + bc + ca)

⇒ 196 - 74 = 2 (ab + bc + ca)

⇒ 2 (ab + bc + ca) = 122

⇒ (ab + bc + ca) = 1222\dfrac{122}{2}

⇒ (ab + bc + ca) = 61.

Hence, (ab + bc + ca) = 61.

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