If A2 + B2 + C2 = 41 and a + B + C = 9; Find Ab + Bc + Ca. - Mathematics

If a² + b² + c² = 41 and a + b + c = 9; find ab + bc + ca.

Sum

(a + b + c)² = (9)²
a² + b² + c² + 2ab + 2bc + 2ca = 81
⇒ 41 + 2(ab + bc + ca) = 81
⇒ 2(ab + bc + ca)
= 81 - 41
= 40
⇒ ab + bc + ca
= 20.

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