一道高二数学题(15)设m,n∈R,比较x^2-x+1与-2m^2-2mx的大小_数学解答

一道高二数学题(15)
设m,n∈R,比较x^2-x+1与-2m^2-2mx的大小

人气：491 ℃　时间：2020-10-02 02:11:28

解答

x^2-x+1>-2m^2-2mx
xx+(2m-1)x+1+2mm>0
f(x)=xx+(2m-1)x+1+2mm
f(x)min=1+2mm-(2m-1)^2/4
=1+2mm-(mm-m+1/4)
=(1/4+mm+m)+1/2>0
x^2-x+1>-2m^2-2mx

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