Question

[Thân An Phương]

so sánh :  x = 13¹⁶+1 / 13¹⁷+1 và y = 13¹⁵+1 / 13¹⁶+1

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Answer 1

[Xyz OLM]

Ta có 13x = \(\frac{13^{17}+13}{13^{17}+1}=1+\frac{12}{13^{17}+1}\)

13y = \(\frac{13^{16}+13}{13^{16}+1}=1+\frac{12}{13^{16}+1}\)

Vì 13¹⁷ + 1 > 13¹⁶ + 1

=> \(\frac{1}{13^{17}+1}< \frac{1}{13^{16}+1}\)

=> \(\frac{12}{13^{17}+1}< \frac{12}{13^{16}+1}\)

=> \(1+\frac{12}{13^{17}+1}< 1+\frac{12}{13^{16}+1}\)

=> 13x < 13y 

=> x < y

Vậy x < y