Question

So sánh : A= 10⁸+2/10⁸-1 và B= 10⁸/10⁸-3

Ai nhanh nhất,đúng nhất mik tik !

Answer 1

\(A=\frac{10^8+2}{10^8-1}\)

\(A=\frac{(10^8-1)+3}{10^8-1}\)

\(A=\frac{10^8-1}{10^8-1}+\frac{3}{10^8-1}=1+\frac{3}{10^8-1}\)

\(B=\frac{10^8}{10^8-3}=\frac{\left(10^8-3\right)+3}{10^8-3}=\frac{10^8-3}{10^8-3}+\frac{3}{10^8-3}=1+\frac{3}{10^8-3}\)

Ta thấy:

\(10^8-1>10^8-3\)

\(\Rightarrow\frac{3}{10^8-1}< \frac{3}{10^8-3}\)

\(\Rightarrow1+\frac{3}{10^8-1}< 1+\frac{3}{10^8-3}\)

\(\Rightarrow A< B\)

P/s: Hoq chắc nên đừng :((

Answer 2

\(A=\frac{10^8+2}{10^8-1}\)

\(A=\frac{10^8-1+3}{10^8-1}\)

\(A=1+\frac{3}{10^8-1}\)

\(B=\frac{10^8}{10^8-3}\)

\(B=\frac{10^8-3+3}{10^8-3}\)

\(B=1+\frac{3}{10^8-3}\)

\(\text{Vì }\frac{3}{10^8-1}< \frac{3}{10^8-3}\)

\(\Rightarrow1+\frac{3}{10^8-1}< 1+\frac{3}{10^8-3}\)

\(\Rightarrow A< B\)