If a + b + c = 12 and ab + bc + ca = 22, find a2 + b2 + c2.
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We know that,
a2 + b2 + c2 = (a + b + c)2 - 2(ab + bc + ca)
Substituting values we get,
a2 + b2 + c2 = (12)2 - 2(22) = 144 - 44 = 100.
Hence, a2 + b2 + c2 = 100.
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If a + b + c = 12 and a2 + b2 + c2 = 100, find ab + bc + ca.
If a2 + b2 + c2 = 125 and ab + bc + ca = 50, find a + b + c.