# Pre-RMO 2014/5

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 Note by Pranshu Gaba
5 years, 3 months ago

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

- 5 years, 3 months ago

But their square is 0

- 1 year, 6 months ago

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

- 5 years, 2 months ago

I 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.

- 5 years, 1 month ago

10

- 4 years, 8 months ago

$\color{#D61F06}{\boxed{10}}$

- 4 years, 5 months ago

10

- 4 years, 5 months ago

10 😊

- 4 years, 4 months ago

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

- 5 years, 3 months ago

10

- 5 years, 3 months ago

10

- 5 years, 3 months ago

- 5 years, 3 months ago

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

- 5 years, 2 months ago

10

- 5 years, 3 months ago

10

- 5 years, 3 months ago