1. 令 x/2 = y/3 = z/4 = k,则有:x = 2k y = 3kz = 4k
所以:(2x + y - z)/(x + y + z) = (2×2k + 3k - 4k)/(2k + 3k + 4k) = 1/3

2因为 x^2 + y^2 + 2x + 4y + 4 = 0
即 ( x + 2x + 1) + (y^2 + 4y + 4) - 1 = 0
所以 (x + 1)^2 + (y + 4)^2 = 1
因为 x, y 为整数,
所以,当 x = -1时, y = -3或y = -5
当 y = - 4时, x = 0 或x = - 2
所以, 当 x = - 1, y = - 3时,x + y = - 1 - 3 = - 4
当 x = - 1, y = - 5时,x + y = - 1 - 5 = - 6
当 x = 0, y = - 4时, x + y = - 4
当 x = - 2, y = -4时, x + y = -2 - 4 = - 6
综上所述, x + y = -4或x + y = -6
3因为 M = 2a^2 + 4b^2 N = 4(ab +a - 1)
所以, M - N = 2a^2 + 4b^2 - 4ab - 4a + 4
= (a^2 - 4a + 4) + (a^2 - 4ab + 4b^2)
= (a - 2)^2 + (a - 2b)^2
因为 (a - 2)^2 ≥0(a - 2b)^2≥0
所以, M - N ≥ 0
所以, M ≥ N