比较两个代数式的大小,1.当x>1时,x^3与想x^2-x+1； 2.x^2+y^2+1与2(x+y-1)

1、x^3-(x^2-x+1)=(x^3-x^2)+(x-1)=(x-1)(x^2+1)
∵x>1 ∴x-1>0 x^2+1>0 ∴(x-1)(x^2+1)>0 ∴x^3-(x^2-x+1)>0
∴x^3>x^2-x+1
2、x^2+y^2+1-2(x+y-1)=(x^2-2x+1)+(y^2-2y+)=(x-1)^2+(y-1)^2
∵ (x-1)^2≥0 (x-1)^2≥0 ∴(x-1)^2+(y-1)^2≥0
∴x^2+y^2+1-2(x+y-1)≥0 ∴x^2+y^2+1≥2(x+y-1)