Question

设x∈R,求x^2+2/√(x^2+1)的最小值

Answer 1

可令t=√(x^2+1).则原式y=-1+t^2+(2/t).===>y+1=t^2+(1/t)+(1/t)≥3*[(t^2)*(1/t)*(1/t)]^(1/3)=3.===>y+1≥3.===>y≥2.等号仅当t=1时取得,即x=±1时取得,故ymin=2.