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Question
If a + b + c = 9 and ab + bc + ca = 23, find the value of a2 + b2 + c2.
Solution
We know that,
`(a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)`
`=> (9)^2 = a^2 + b^2 + c^2 + 2(23)`
`=> 81 = a^2 + b^2 + c^2 + 46` [∵ a + b + c = 9 and (ab + bc + ca = 23)]
`=> a^2 + b^2 + c^2 = 81 - 46`
`=> a^2 + b^2 + c^2 = 35`
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