Question

一道史上最难得函数题!已知实数a,b,c满足条件a/(m+2)+b/(m+1)+c/m=0,其中m是正数,对于f(x)=

Answer 1

这个题挺有意思的.

第一问：

a/(m+2)+b/(m+1)+c/m=0

此式两边同乘以m

得到am/(m+2)+bm/(m+1)+c=0

∴bm/(m+1)+c=-am/(m+2)

af[m/(m+1)]

=a{am^2/(m+1)^2+[bm/(m+1)+c]}

=a[am^2/(m+1)^2-am/(m+2)]

=(a^2)(m^2)[1/(m+1)^2-1/m(m+2)]

∵(m+1)^2-m(m+2)=m^2+2m+1-m^2-2m=1>0

∴1/(m+1)^2-1/m(m+2)0

∴af[m/(m+1)]0,与①式相乘

得：[af(0)]{af[m/(m+1)]}=(a^2)f(0)f[m/(m+1)]0,与①式相乘

得：=(a^2)f(1)f[m/(m+1)]