比较【x2-√2x+1】【x2+√2x+1】与【x2-x+1】【x2+x+1】大小

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比较【x2-√2x+1】【x2+√2x+1】与【x2-x+1】【x2+x+1】大小比较【x2-√2x+1】【x2+√2x+1】与【x2-x+1】【x2+x+1】大小比较【x2-√2x+1】【x2+√2

比较【x2-√2x+1】【x2+√2x+1】与【x2-x+1】【x2+x+1】大小
比较【x2-√2x+1】【x2+√2x+1】与【x2-x+1】【x2+x+1】大小

比较【x2-√2x+1】【x2+√2x+1】与【x2-x+1】【x2+x+1】大小
【x2-√2x+1】【x2+√2x+1)=x^4-2x-1
【x2-x+1】【x2+x+1】=【x^2+1-x】【x2+1+x】=(x^2+1)^2-x^2=x^4+2x^2+1-x^2=x^4+x^2+1
两者相减:
x^4-2x-1 - (x^4+x^2+1)=-2x-1-x^2-1=-(x^2+2x+2)
x^2+2x+2中,deta=4-80
-(x^2+2x+2)

(x²-√2x+1)(x²-√2x+1)
=(x²+1)²-(√2x)²
=x^4+2x²+1-2x²
=x^4+1
(x²-x+1)(x²+x+1)
=x^4+2x²+1-x²
=x^4+x²+1
0<=x²
所以x^4+1<=x^4+x²+1
(x²-√2x+1)(x²-√2x+1)<=(x²-x+1)(x²+x+1)