If real numbers a,b,c,d,ea, b, c, d, ea,b,c,d,e satisfy
a+1=b+2=c+3=d+4=e+5=a+b+c+d+e+3,a + 1 = b + 2 = c + 3 = d + 4 = e + 5 = a + b + c + d + e + 3,a+1=b+2=c+3=d+4=e+5=a+b+c+d+e+3,
what is the value of a2+b2+c2+d2+e2a^2 + b^2 + c^2 + d^2 + e^2a2+b2+c2+d2+e2?
This note is part of the set Pre-RMO 2014
Note by Pranshu Gaba 6 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.
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But their square is 0
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
I did this sum by solving each part individually i.e I obtained every part in terms of d d d and then I solved the equation to get the answer as 10.
10
10\color{#D61F06}{\boxed{10}}10
10 😊
the answer is 10..
Equate everything to k and substitute accordingly.The answer is 10.
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Easy Math Editor
This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.
When posting on Brilliant:
*italics*or_italics_**bold**or__bold__paragraph 1
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[example link](https://brilliant.org)> This is a quote# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"\(...\)or\[...\]to ensure proper formatting.2 \times 32^{34}a_{i-1}\frac{2}{3}\sqrt{2}\sum_{i=1}^3\sin \theta\boxed{123}Comments
Solving the equations a=2,b=1,c=o,d=-1,e=-2.Thus the answer is 10.
Log in to reply
But their square is 0
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
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.
10
10
10
10 😊
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
10
10
the answer is 10..
Equate everything to k and substitute accordingly.The answer is 10.
10
10