Question

So Sánh :

A=\(\frac{10^{50}+2}{10^{50}-1}\)và B=\(\frac{10^{50}}{10^{50}-3}\)

Answer 1

Ta có:

\(A=\frac{10^{50}+2}{10^{50}-1}=\frac{10^{50}-1+3}{10^{50}-1}=1+\frac{3}{10^{50}-1}\)

\(B=\frac{10^{50}}{10^{50}-3}=\frac{10^{50}-3+3}{10^{50}-3}=1+\frac{3}{10^{50}-3}\)

Vì \(10^{50}-1>10^{50}-3\Rightarrow\frac{3}{10^{50}-1}< \frac{3}{10^{50}-3}\)(2 phân số có cùng tử số, mẫu số của phân số nào lớn hơn thì phân  

                                                                                             số đó nhỏ hơn)

\(\Rightarrow1+\frac{3}{10^{50}-1}< 1+\frac{3}{10^{50}-3}\Rightarrow A< B\)     

Answer 2

\(A=\frac{10^{50}+2}{10^{50}-1}=\frac{10^{50}-1+3}{10^{50}-1}=1+\frac{3}{10^{50}-1}.\)

\(B=\frac{10^{50}}{10^{50}-3}=\frac{10^{50}-3+3}{10^{50}-3}=1+\frac{3}{10^{50}-3}.\)

Do 10⁵⁰-1 > 10⁵⁰-3 ; => \(1+\frac{3}{10^{50}-3}>1+\frac{3}{10^{50}-1}\)

=> B > A

Answer 3

\(A=\frac{10^{50}+2}{10^{50}-1}=\frac{10^{50}-1+3}{10^{50}-1}=\)\(\frac{10^{50}-1}{10^{50}-1}+\frac{3}{10^{50}-1}\)\(=1+\frac{3}{10^{50}-1}\)

\(B=\frac{10^{50}}{10^{50}-3}=\frac{10^{50}-3+3}{10^{50}-3}\)\(=\frac{10^{50}-3}{10^{50}-3}+\frac{3}{10^{50}-3}\)\(=1+\frac{3}{10^{50}-3}\)

Ta có: 1<3 suy ra \(10^{50}-1>10^{50}-3\)

Suy ra\(\frac{3}{10^{50}-1}< \frac{3}{10^{50}-3}\)

Suy ra \(1+\frac{3}{10^{50}-1}< 1+\frac{3}{10^{50}-3}\)

Suy ra A<B