Countdown to 2014: Problem #3

Level pending

Let S S be the sum of all real root(s) for the equation x − 2014 + ( x − 2014 ) 2014 + ∣ x − 2014 ∣ = 0 \sqrt{x-2014}+(x-2014)^{2014}+|x-2014|=0 What is S 38 \frac{S}{38} ?


The answer is 53.

Wee Xian Bin by Wee Xian Bin , 25, Singapore

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2 solutions

Budi Utomo
Dec 31, 2013

because there was (x-2014)^1/2 and the solution has 0, so x>=2014. And i think it problem has 1 solution x = 2014. So , S = x ---> S/38 = 2014/38 = 53

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Bogdan Simeonov
Dec 31, 2013

Obviously 2014 ≤ x 2014\le x (because if x<2014,the square root is a complex number) and we see that 2014 is a solution.For x>2014 ,the left side is positive and the right one is zero-contradiction.So S=2014 and 2014/38=53.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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