Question

利用均值定理求最值若x>-1,求log2[x+1/(x+1)+3]的最小值

Answer 1

log2[x+1/(x+1)+3]=log2[(x+1)+1/(x+1)+2]

>=log2[2*根号下(x+1)*(1/(x+1))+2]=log2(4)=2

当且仅当x+1=1/(x+1)时取等号.

所以原式min值为2