Complex number whose real and imaginary parts $x$ and $y$ are integers and satisfy the equation $3x^2 - |xy| - 2y^2 + 7 = 0$
Step-by-Step Solution
Key Concept: Transform constraints by substitution to convert a restricted counting problem into standard binomial coefficient form.
Let $a_0, a_1, a_2, a_3$ denote the numbers of objects in consecutive groups. Given constraints $a_0, a_3 \geq 0$, $a_1, a_2 \geq 1$, and $a_0 + a_1 + a_3 = n - 3$, we use substitution to obtain ${}^{n-1}C_{n-1} = {}^{n-2}C_1 = \frac{(n-2)(n-3)(n-4)}{6}$. Alternatively, ${}^{n-2}C_1 = {}^{n-3}C_1 + {}^{n-2}C_2$.
Correct Answer: 2,3