Question

tìm nghiệm nguyên thỏa:

(x-18)¹⁹(x-19)¹⁸(x-2018)²⁰¹⁹<=0

Answer 1

Lời giải:

\((x-18)^{19}(x-19)^{18}(x-2018)^{2019}\leq 0\)

\(\Leftrightarrow (x-18)^{18}(x-18)(x-19)^{18}(x-2018)^{2018}(x-2018)\leq 0\)

\(\Leftrightarrow [(x-18)^9(x-19)^9(x-2018)^{1009}]^2(x-18)(x-2018)\leq 0\)

\(\Leftrightarrow (x-18)(x-2018)\leq 0\)

\(\Rightarrow \left[\begin{matrix} x-18\leq 0; x-2018\geq 0\\ x-18\geq 0; x-2018\leq 0\end{matrix}\right.\Leftrightarrow \left[\begin{matrix} 2018\leq x\leq 18(\text{vô lý})\\ 2018\geq x\geq 18\end{matrix}\right.\)

Vậy \(2018\geq x\geq 18\). Mà $x$ nguyên nên \(x\in\left\{18; 19;20; 21;....; 2018\right\}\)