Question

so sánh :

x = 19¹⁷+1 / 19¹⁶+1 và y = 19¹⁶+1 / 19¹⁵+1 

Mình đag cần rất gấp

Answer 1

\(\frac{x}{19}=\frac{19^{17}+1}{19^{17}+19}=1-\frac{18}{19^{17}+19}\)

\(\frac{y}{19}=\frac{19^{16}+1}{19^{16}+19}=1-\frac{18}{19^{16}+19}\)

Nhận thấy 19¹⁷ + 19 > 19¹⁶ + 19

=> \(\frac{18}{19^{17}+19}< \frac{18}{19^{16}+19}\)

=> \(-\frac{18}{19^{17}+19}>-\frac{18}{19^{16}+19}\)

=> \(1-\frac{18}{19^{17}+19}>1-\frac{18}{19^{16}+19}\)

=> \(\frac{x}{19}>\frac{y}{19}\)

=> x > y

Vậy x > y

Answer 2

Ta có : \(\frac{x}{19}=\frac{19^{17}+1}{19^{17}+19}=1-\frac{18}{19^{17}+19}\)

\(\frac{y}{19}=\frac{19^{16}+1}{19^{16}+19}=1-\frac{18}{19^{16}+19}\)

Vì\(\frac{18}{19^{17}+19}< \frac{18}{19^{16}+19}\)\(\Rightarrow\frac{x}{19}>\frac{y}{19}\)

mà \(x,y>0\)

\(\Rightarrow x>y\)