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Question
If a2 + b2 + c2 = 35 and ab + bc + ca = 23; find a + b + c.
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Solution
We know that
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) ...(1)
Given that, a2 + b2 + c2 = 35 and ab + bc + ca = 23
We need to find a + b + c :
Substitute the values of (a2 + b2 + c2) and (ab + bc + ca)
in the identity (1), we have
(a + b + c)2 = 35 + 2(23)
⇒ (a + b + c)2 = 81
⇒ a + b + c = `+-sqrt81`
⇒ a + b + c = `+-9`
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