If a + b + c = 12 and a2 + b2 + c2 = 100, find ab + bc + ca.
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We know that,
a2 + b2 + c2 = (a + b + c)2 - 2(ab + bc + ca)
Substituting values we get,
⇒ 100 = 122 - 2(ab + bc + ca)
⇒ 100 = 144 - 2(ab + bc + ca)
⇒ 2(ab + bc + ca) = 144 - 100
⇒ 2(ab + bc + ca) = 44
⇒ (ab + bc + ca) = 22.
Hence, ab + bc + ca = 22.
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