1,由y=x/（ax²+b）,a>0,b>0,故ax²+b>0,故x∈R,
故ayx²+by=x,故ayx²-x+by=0,
當y=0時,x=0,
當y≠0時,由a>0,b>0,故ay≠0,Δ=1-4ay by≥0,故4aby ²≤1,故y ²≤1/4ab,
故-√(ab)/(2ab)≤y ≤√(ab)/(2ab),故值域[-√(ab)/(2ab),√(ab)/(2ab)]
2,由y=ax²+x+1/（x+1）,
故y的導數(shù)=2ax+1-1/（x+1）²
=[2ax（x+1）²+（x+1）²-1]/（x+1）²=x[2ax²+(4a+1)x+2a+2]/（x+1）²,
故Δ=(4a+1)²-8a(2a+2)=-8a+1,
（1）當Δ=-8a+11/8,2ax²+(4a+1)x+2a+2>0,令y的導數(shù)=0,故x=0,
若x0,故x=0時,y的最小值為1,
（2）當Δ=-8a+1=0時,即a=1/8,方程根為x=-2,由x>-1,
若-10,即a