if a + b + c = 9 and ab + bc+ ca = 26 find a^2 + b^2 + c^2 .
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Given (a + b + c) = 9 and (ab + bc + ca) = 26
(a + b + c)2 = 92
⇒ a2 + b2 + c2 + 2(ab + bc + ca) = 81
⇒ a2 + b2 + c2 + 2(26) = 81
⇒ a2 + b2 + c2 + 52 = 81
⇒ a2 + b2 + c2 = 81 − 52 = 29
(a + b + c)2 = 92
⇒ a2 + b2 + c2 + 2(ab + bc + ca) = 81
⇒ a2 + b2 + c2 + 2(26) = 81
⇒ a2 + b2 + c2 + 52 = 81
⇒ a2 + b2 + c2 = 81 − 52 = 29
thanks sexyjas
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(a + b + c)2 = 92
⇒ a2 + b2 + c2 + 2(ab + bc + ca) = 81
⇒ a2 + b2 + c2 + 2(26) = 81
⇒ a2 + b2 + c2 + 52 = 81
⇒ a2 + b2 + c2 = 81 − 52 = 29