# 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
3 years, 8 months ago

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

- 3 years, 8 months ago

10 😊

- 2 years, 10 months ago

10

- 2 years, 10 months ago

$$\color{red}{\boxed{10}}$$

- 2 years, 10 months ago

10

- 3 years, 1 month 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.

- 3 years, 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

- 3 years, 8 months ago

- 3 years, 8 months ago

10

- 3 years, 8 months ago

10

- 3 years, 8 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

- 3 years, 8 months ago

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

- 3 years, 8 months ago

10

- 3 years, 8 months ago

10

- 3 years, 8 months ago