2016全国高中数学联赛安徽省初赛（PDF含答案）

(b+c) +b2c2￡￡?!ü?¤?34a2(b2+c2)≥32a2bc?a2(b?c)2≥0?(16?)??a?ò¤á?7?^?′a(b?c) = 0?'u??^????óy{??(22?)12.|÷v1≤mn?nm≤mn?¤k??êé(m,n)?)???ky2ü?ún"ún1μf(x) =lnxx3(0, e]tüNO§3[e,∞)tüN~?y2μf0(x) =1?lnxx§3(0, e)t?u0§3(e,∞)t?u0?(3?)ún2μ?x >0?§ln(1 +x)< x?AO§?x=1n§K(1 +1n)n< e?y2μ?f(x) =x?ln(1 +x)"?x >0?§f0(x) =x1+x>0§?f(x)üNO?2df(0) = 0§?x >ln(1 +x)?(6?)￡??ˉK"?aún1§mn> nm?lnmm>lnnn§k±eA??/??/?μn= 1§m≥2?(m,n)t÷vK??(8?)?/?μm= 2§n≥5??g(x) = 2x?x2?2x§x≥5§Kg0(x) = 2xln 2?2x?2>0?dg(5) =?3§g(6) = 16§??÷vK??(m,n)?k(2,5)?(13?)?/nμm= 3§n= 2?′?y(3,2)÷vK??(15?)?/oμm≥3§n≥m+ 1??g(x) =mx?xm?mx??x≥m+ 1?§g0(x) =mxlnm?mxm?1?m > xm?mxm?1?m≥xm?1?m >0§g(x)üNO??d§g(n)≥h(m) =mm+1?(m+ 1)m?m(m+ 1) =mm[m?(1 +1m)m]?m(m+ 1)??m= 3?§h(m) = 5??m≥4?§?aún2§h(m)> mm?m(m+1)>0??(m,n)÷vK??nt§¤k÷vK????êé?{(m,1),(2,5),(3,2)|m≥2}?(22?)