(i) 2a+2b = 2(0)+2(-1) = 0-2=-2 [putting a=0,b=-1]
(ii) 2a2+b2+1 = 2(0)2+(-1)2+1 = 2×0+1+1 = 0+2 = 2 [putting a=0,b=-1]
(iii) 2a2b+2ab2+ab = 2(0)2(-1)+2(0)(-1)2+(0)(-1) = 0+0+0 = 0 [putting a=0,b=-1]
(iv) a2+ab+2 = (0)2+(0)(-1)+2 = 2 [putting a = 0,b=-1]
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 \( \frac{k}{\alpha^2 \beta^2} = ? \)