(1) f(x)=ax^2+1f'(x)=2axf'(1)=2ag(x)=x^3+bxg'(x)=3x^2+bg'(1)=3+b在(1,c)具有公切线f'(1)=g'(1)2a=3+b.(1)f(1)=g(1)a+1=1+ba=b.(2)联解(1)(2)：a=b=3(2) a^2=4bb=a^2/4h(x)=f(x)+g(x)=ax^2+1+x^3+a^2/4x=x(x^2+ax...