A 200 followers problem
Number Theory
Level
3
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 ?
The answer is 10.
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Let a + 1 = b + 2 = c + 3 = d + 4 = e + 5 = a + b + c + d + e + 3 = k .
Now a + 1 = k .
Rearranging we get a = k − 1 .
Similarly, b = k − 2 , c = k − 3 , d = k − 4 , e = k − 5 .
Also a + b + c + d + e + 3 = k .
Substituting the values in we get k = 3 .
Now a = 2 , b = 1 , c = 0 , d = − 1 , e = − 2 .
Therefore a 2 + b 2 + c 2 + d 2 + e 2 = 1 0 .