Question

Cho A=2016^2016+2/2016^2016-1 và B=2016^2016/2016^2016-3

Answer 1

Ta có:A=\(\frac{2016^{2016}+2}{2016^{2016}-1}\)>1

=>A<\(\frac{2016^{2016}+2-2}{2016^{2016}-1-2}\)=\(\frac{2016^{2016}}{2016^{2016}-3}\)=B

=>A<B(công thức nếu \(\frac{a}{b}\)>1 thì \(\frac{a}{b}\)<\(\frac{a-n}{b-n}\)(nEN)

CM công thức:

Ta có \(\frac{a}{b}\)>1=>a>b=>a=b+n(nEN)

Ta so sánh \(\frac{a}{b}\) và \(\frac{a-n}{b-n}\)(nEN)

Mà a*(b-n)=ab-an=ab-(b+n)*n=ab-(bn+n²)=ab-bn-n²

       b*(a-n)=ba-bn

Vì ab-bn-n²<ba-bn

=>\(\frac{a}{b}\)<\(\frac{a-n}{b-n}\)