Question

证明:若x^2-y^2+x-5y-6≠0,则x-y≠2.

Answer 1

证明：

x^2-y^2+x-5y-6≠0

(x+1/2)^2-(y+5/2)^2-1/4+25/4-6≠0

(x+1/2)^2-(y+5/2)^2≠0

[(x+1/2)+(y+5/2)][(x+1/2)-(y+5/2)]≠0

(x+y+3)(x-y-2)≠0

x+y≠-3且x-y≠2