Permutations & Combinations
Integer solutions of multiplicative equation
Grade Class 12
Question:
The number of solutions $(n_1, n_2)$ which satisfy $n_1 n_2 = 2n_1 - n_2$, where $n_1, n_2 \in \mathbb{I}$ (integers) is
Step-by-Step Solution
Key Concept: Rearrange: $n_1 n_2 + n_2 = 2n_1 \Rightarrow n_2(n_1+1)=2n_1$. Solve for $n_2=\frac{2n_1}{n_1+1}=2-\frac{2}{n_1+1}$.
$(n_1,n_2)\in\{(0,0),(1,1),(-2,4),(-3,3)\}$: 4 solutions.
Correct Answer: 4