Question

[Vũ Trí Thuận]

So sánh :

A = \(\frac{53^{30}}{53^{30}-6}\)

B = \(\frac{53^{30}+4}{53^{30}-2}\)

Answer 1

[Nguyễn Tuấn Minh]

\(A=\frac{53^{30}}{53^{30}-6}=\frac{53^{30}-6+6}{53^{30}-6}=1+\frac{6}{53^{30}-6}\)

\(B=\frac{53^{30}-4}{53^{30}-2}=\frac{53^{30}-2+6}{53^{30}-2}=1+\frac{6}{53^{30}-2}\)

Vì 53³⁰-6<53³⁰-2 nên \(\frac{6}{53^{30}-6}>\frac{6}{53^{30}-2}\)

=> A>B

Answer 2

[Hoàng Quỳnh Phương]

Ta có:

A=\(\frac{53^{30}-6+6}{53^{30}-6}\)=\(1-\frac{6}{5^{30}-6}\)

B=\(\frac{53^{30}-2+6}{53^{30}-2}\)=\(1-\frac{6}{5^{30}-2}\)

Vì 53³⁰-6<53³⁰-2 nên \(\frac{6}{53^{30}-6}\)>\(\frac{6}{53^{30}-2}\)

=> \(1-\frac{6}{53^{30}-6}\)\(< 1-\frac{6}{5^{30}-2}\)

Vậy A<B