Question

So sánh 

a. 5\(^{37}\) và 11\(^{24}\) 

b. \(\frac{a}{b}\) và \(\frac{a+2012}{b+2012}\)

Answer 1

a) Ta có:

5³⁷ > 5³⁶ = (5³)¹² = 125¹²

11²⁴ = (11²)¹² = 121¹²

Vì 5³⁷ > 125¹² > 121¹²

=> 5³⁷ > 11²⁴

b) + Nếu a < b

=> 2012a < 2012b

=> 2012a + ab < 2012b + ab

=> a.(b + 2012) < b.(a + 2012)

=> \(\frac{a}{b}< \frac{a+2012}{b+2012}\)

+ Nếu a = b

=> 2012a = 2012b

=> 2012a + ab = 2012b + ab

=> a.(b + 2012) = b.(a + 2012)

=> \(\frac{a}{b}=\frac{a+2012}{b+2012}\)

+ Nếu a > b

=> 2012a > 2012b

=> 2012a + ab > 2012b + ab

=> a.(b + 2012) > b.(a + 2012)

=> \(\frac{a}{b}>\frac{a+2012}{b+2012}\)