Given:
2(a2+ab)+3-ab
⇒ 2a2+2ab+3-ab
⇒ 2a2+2ab-ab+3
⇒ 2a2+ab+3
⇒ 2(5)2+(5)(-3)+3
⇒ 2×25-15+3 [putting a=5, b=-3]
⇒ 50-15+3
⇒ 38
If \( x, y \) are two positive integers such that \( x + y = 20 \) and the maximum value of \( x^3 y \) is \( k \) at \( x = a, y = \beta \), then \( \frac{k}{\alpha^2 \beta^2} = ? \)