Question

So sánh bằng nhiều cách khác nhau

a/ \(\frac{7}{15}và\frac{15}{23}\)

b/ \(x=\frac{13^{16}+1}{13^{17}+1}\)và \(y=\frac{13^{15}+1}{13^{16}+1}\)

mk lm cái nì rùi nè, giải giúp mk thử nha

để mk xem lại có đúng ko nha

ơn trước nha

Answer 1

a. \(\frac{7}{15}< \frac{7}{14}=\frac{1}{2};\frac{15}{23}>\frac{15}{30}=\frac{1}{2}\text{ hay }\frac{7}{15}< \frac{1}{2}< \frac{15}{23}\)

Vậy \(\frac{7}{15}< \frac{15}{23}\).

b. \(x=\frac{13^{16}+1}{13^{17}+1}\Rightarrow13x=\frac{13^{17}+13}{13^{17}+1}=1+\frac{12}{13^{17}+1}\)

\(y=\frac{13^{15}+1}{13^{16}+1}\Rightarrow13y=\frac{13^{16}+13}{13^{16}+1}=1+\frac{12}{13^{16}+1}\)

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

Mà 1 = 1 => \(1+\frac{12}{13^{17}+1}< 1+\frac{12}{13^{16}+1}\text{ hay }13x< 13y\)

=> x < y.

Answer 2

ơn nha