Welcome new year 2018

Algebra Level 2

Find the 2-digit positive integer x x such that x 2 + 18 x − 17 x^2 +18 x - 17 is divisible by 2018.


The answer is 37.

Ossama Ismail by Ossama Ismail , 63, Egypt

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1 solution

Chew-Seong Cheong
Dec 18, 2017

Let us check the smallest allowable x x as follows:

x 2 + 18 x − 17 = 2018 x 2 + 18 x − 2035 = 0 ( x − 37 ) ( x + 55 ) = 0 ⟹ x = 37 \begin{aligned} x^2+18x-17 & = 2018 \\ x^2+18x-2035 & = 0 \\ (x-37)(x+55) &= 0 \\ \implies x & = \boxed{37} \end{aligned}

Wishing Everybody A Happy 2018. \Large \color{#69047E} \textit{Wishing Everybody A Happy 2018.}

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Wishing you a year full of happiness and prosperity

Ossama Ismail - 3 years, 5 months ago

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