(i) 4p+7 = 4(-2)+7 = -8+7 = -1 [putting p = -2]
(ii) -3p2 + 4p+7 = -3(-2)2+4(-2)+7 = -3×4-8+7 = -12-8+7 = -20+7 = -13 [putting p = -2]
(iii) -2p3-3p2+4p+7 = -2(-2)3-3(-2)2+4(-2)+7 = -2×(-8)-3×4-8+7 = 16-12-8+7 = -20+23 = 3 [putting p = -2]
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 \( \frac{k}{\alpha^2 \beta^2} = ? \)