比较(x平方-根号2x+1)(x平方+根号2x+1)与(x平方-x+1)(平方x+x+1)的大小
问题描述：
比较(x平方-根号2x+1)(x平方+根号2x+1)与(x平方-x+1)(平方x+x+1)的大小
答
[(x^2-根号2x+1)][(x^2+根号2x+1)]-[(x^2-(x+1)][(x^2+(x+1)]
=x^4-2x-1-(x^4-x^2-2x-1)
=x^2≥0
所以
[(x^2-根号2x+1)][(x^2+根号2x+1)]≥[(x^2-(x+1)][(x^2+(x+1)]
答
(x^2-√2x+1)(x^2+√2x+1)-(x^2-x+1)(x^2+x+1)
=[(x^2+1)^2-(√2x)^2]-[(x^2+1)^2-x^2]
=(x^2+1)^2-(√2x)^2-(x^2+1)^2+x^2
=x^2-(√2x)^2
=x^2-2x^2
=-x^2