1 设y-m=k(3x+n) 代数得7-m=9k+kn 4-m=6k+kn
解方程组得 k=1 m+n=-2 故y=3x-2
2 原式=2^50+(-2)^49+2^48+(-2)^47……+2^2+(-2)+1
=2^49(2-1)+2^47(2-1)+……+2(2-1)+1
=1+2*(1-4^25)/(1-4)=1/3+2^51/3
3 由已知：a,b,c两正一负,故abc=-1
原式=（-1）^1999/(a^2*b^2*c^2/|abc|^2)=-1
4 原式=[x+(2y-1)][x-(2y-1)]-[x-(2y+1)]^2
=x^2-(2y-1)^2-[x^2-2x(2y+1)+(2y+1)^2]
=x^2-4y^2+4y-1-x^2+4xy+2x-4y^2-4y-1=4xy+2x-8y^2-2
5 原式=1/2(2*a^2+2*b^2+2*c^2-2*ab-2*bc-2*ac)
=1/2[(a^2-2*ab+b^2)+(a^2-2*ac+c^2)+(c^2-2*cb+c^2)
=1/2[(a-b)^2+(a-c)^2+(b-c)^2]=1/2[1+1+1]=1.5
6 原式=[(a+c)-(b-d)][(a+c)+(b-d)]=(a+c)^2-(b-d)^2
=a^2+2ac+c^2-b^2+4bd-d^2