Question

So sánh:

\(A=\frac{67^{2016}}{67^{2016}-11}\) và \(B=\frac{67^{2016}+13}{67^{2016}+2}\)

Ai nhanh và có lời giải mik tick cho

Answer 1

Ta có:

\(A=\frac{67^{2016}}{67^{2016}-11}=1+\frac{11}{67^{2016}-11}\)

\(B=\frac{67^{2016}+13}{67^{2016}+2}=1+\frac{11}{67^{2016}+2}\)

Vì \(67^{2016}-11< 67^{2016}+2\) nên \(\frac{11}{67^{2016}-11}>\frac{11}{67^{2016}+2}\Rightarrow1+\frac{11}{67^{2016}-11}>1+\frac{11}{67^{2016}+2}\)

Vậy A > B