If (a + b + c)= 17, and (a2 + b2 + c2) = 115, find the value of (a + b)2 + (b + c)2 + (c + a)2.
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Correct answer: D
Explanation
The correct answer is option 4 i.e. 404.
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
⇒ 172 = 115 + 2(ab + bc + ca)
⇒ 2(ab + bc + ca) = 289 - 115 = 174
⇒ ab + bc + ca = 174/2 = 87
Now, (a + b)2 + (b + c)2 + (c + a)2 = 2(a2 + b2 + c2) + 2(ab + bc + ca)
= 2(115) + 2(87)
= 230 + 174
= 404
Hence, the required value is 404.