If a + b + c = 12 and ab + bc + ca = 47 , find the value of a2 + b2 + c2
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We know,
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
⇒ a2 + b2 + c2 = (a + b + c)2 – 2 (ab + bc + ca)
⇒ a2 + b2 + c2 = (12)2 – 2 × 47 = 144 – 94 = 50 [a + b + c = 12 and ab + bc + ca = 47]
Thus, the value of a2 + b2 + c2 is 50
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
⇒ a2 + b2 + c2 = (a + b + c)2 – 2 (ab + bc + ca)
⇒ a2 + b2 + c2 = (12)2 – 2 × 47 = 144 – 94 = 50 [a + b + c = 12 and ab + bc + ca = 47]
Thus, the value of a2 + b2 + c2 is 50
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