Question

证明：若x^2-y^2+x-5y-6不等于0,则x-y不等于2

Answer 1

因为x^2-y^2+x-5y-6不等于0

所以

x^2-y^2+x-5y-6

=x^2-y^2+x-5y-(25/4-1/4)

=(x^2+x+1/4)-(y^2+5y+25/4)

=(x+1/2)^2-(y+5/2)^2

=(x+1/2+y+5/2)(x+1/2-y-5/2)

=(x+y+3)(x-y-2)不等于0

所以

x+y+3不等于0

x-y-2不等于0

所以

x+y不等于-3

x-y不等于2