Tìm x, y ∈ ℕ, biết: (2x + 1)(y – 3) = 10

Câu 3: Tìm x, y ∈ ℕ, biết: (2x + 1)(y – 3) = 10.

Trả lời

(2x + 1)(y – 3) = 10 = 1.10 = 10.1 = 2.5 = 5.2.

Ta có:

⦁ $\left\{\begin{array}{l}2x+1=10\\ y-3=1\end{array}\right.\iff \left\{\begin{array}{l}x=\frac{9}{2}\\ y=4\end{array}\right.$  (loại vì x ∉ ℕ).

⦁ $\left\{\begin{array}{l}2x+1=1\\ y-3=10\end{array}\right.\iff \left\{\begin{array}{l}x=0\\ y=13\end{array}\right.$  (nhận).

⦁ $\left\{\begin{array}{l}2x+1=2\\ y-3=5\end{array}\right.\iff \left\{\begin{array}{l}x=\frac{1}{2}\\ y=8\end{array}\right.$  (loại vì x ∉ ℕ).

⦁ $\left\{\begin{array}{l}2x+1=5\\ y-3=2\end{array}\right.\iff \left\{\begin{array}{l}x=2\\ y=5\end{array}\right.$  (nhận).

Vậy (x; y) ∈ {(0; 13), (2; 5)}.