If a + b + c = 12 and a2 + b2 + c2 = 50; find ab + bc + ca.
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By formula,
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca).
Substituting values we get :
⇒ 122 = 50 + 2(ab + bc + ca)
⇒ 144 = 50 + 2(ab + bc + ca)
⇒ 2(ab + bc + ca) = 144 - 50
⇒ 2(ab + bc + ca) = 94
⇒ ab + bc + ca = 47.
Hence, ab + bc + ca = 47.
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