Question

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

Answer 1

(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