If real numbers \(a, b, c, d, e\) satisfy

\[a + 1 = b + 2 = c + 3 = d + 4 = e + 5 = a + b + c + d + e + 3,\]

what is the value of \(a^2 + b^2 + c^2 + d^2 + e^2\)?

This note is part of the set Pre-RMO 2014

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## Comments

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TopNewestI did this sum by solving each part individually i.e I obtained every part in terms of \( d \) and then I solved the equation to get the answer as 10.

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let this all be equal to k a=k-1 ,b=k-2 ,c=k-3, d=k-4 ,e=k-5 now substituting these values in last equation we get a,b,c,d,e

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Solving the equations a=2,b=1,c=o,d=-1,e=-2.Thus the answer is 10.

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But their square is 0

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10 😊

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10

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\(\color{red}{\boxed{10}}\)

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10

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the answer is 10..

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10

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10

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let this all be equal to k a=k-1 ,b=k-2 ,c=k-3, d=k-4 ,e=k-5 now substituting these values in last equation we get a,b,c,d,e

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Equate everything to k and substitute accordingly.The answer is 10.

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10

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10

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