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Question
If a + b + c = 9 and ab + bc + ca = 26, find a2 + b2 + c2.
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Solution
Given, a + b + c = 9 and ab + bc + ca = 26 ...(i)
Now, a + b + c = 9
On squaring sides, we get
(a + b + c)2 = (9)2
⇒ a2 + b2 + c2 + 2ab + bc + ca = 81 ...[Using identity, (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca]
⇒ a2 + b2 + c2(ab + bc + ca) = 81
⇒ a2 + b2 + c2 + 2(26) = 81 ...[From equation (i)]
⇒ a2 + b2 + c2 = 81 – 52 = 29
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