Mina giúp mk vs!!!!!!!!!!
1)So sánh
a)\(\dfrac{12}{47}và\dfrac{11}{53}\) b)\(\dfrac{456}{461}và\dfrac{123}{128}\) c)\(\dfrac{12}{47}và\dfrac{19}{77}\)
d)\(A=\dfrac{13^{15}+1}{13^{16}+1}và\) \(B=\dfrac{13^{16}+1}{13^{17}+1}\)
P/s:Cherry Võ tag Trần Huyền Trang giùm cái please
a) \(\dfrac{12}{47}\) và \(\dfrac{11}{53}\)
Ta có: \(\dfrac{11}{47}>\dfrac{11}{53}\) mà \(\dfrac{12}{47}>\dfrac{11}{47}\)
\(\Rightarrow\dfrac{12}{47}>\dfrac{11}{53}\)
a) Ta có :\(\dfrac{12}{47}>\dfrac{12}{48}=\dfrac{1}{4}=\dfrac{11}{44}>\dfrac{11}{53}\)
\(\Rightarrow\dfrac{12}{47}>\dfrac{11}{53}\)
b) Ta có : \(\dfrac{456}{461}=1-\dfrac{5}{461}\)
\(\dfrac{123}{128}=1-\dfrac{5}{128}\)
Vì \(\dfrac{5}{461}< \dfrac{5}{128}\Rightarrow1-\dfrac{5}{461}>1-\dfrac{5}{128}\)
\(\Rightarrow\dfrac{456}{461}>\dfrac{123}{128}\)
c) Ta có :\(\dfrac{12}{47}>\dfrac{12}{48}=\dfrac{1}{4}=\dfrac{19}{76}>\dfrac{19}{77}\)
=> \(\dfrac{12}{47}>\dfrac{19}{77}\)
d) Ta có : \(13A=13.\dfrac{13^{15}+1}{13^{16}+1}=\dfrac{13^{16}+13}{13^{16}+1}=\dfrac{13^{16}+1+12}{13^{16}+1}=1+\dfrac{12}{13^{16}+1}\)
\(13B=13.\dfrac{13^{16}+1}{13^{17}+1}=\dfrac{13^{17}+13}{13^{17}+1}=\dfrac{13^{17}+1+12}{13^{17}+1}=1+\dfrac{12}{13^{17}+1}\)
Ta thấy : \(\dfrac{12}{13^{16}+1}>\dfrac{12}{13^{17}+1}\Rightarrow1+\dfrac{12}{13^{16}+1}>1+\dfrac{12}{13^{17}+1}\Rightarrow\dfrac{13^{15}+1}{13^{16}+1}>\dfrac{13^{16}+1}{13^{17}+1}\)
a) Ta có : \(\dfrac{12}{47}>\dfrac{12}{53}>\dfrac{11}{53}\) \(\Leftrightarrow\dfrac{12}{47}>\dfrac{11}{53}\) b) Ta có : \(\dfrac{456}{461}=\dfrac{461-5}{461}=1-\dfrac{5}{461}\) \(\dfrac{123}{128}=\dfrac{128-5}{128}=1-\dfrac{5}{128}\) Do \(1-\dfrac{5}{461}>1-\dfrac{5}{128}\) \(\Rightarrow\dfrac{456}{461}>\dfrac{123}{128}\) c) Ta có: \(\dfrac{12}{47}\) > \(\dfrac{12}{48}=\dfrac{1}{4}\) \(\dfrac{19}{77}< \dfrac{19}{76}=\dfrac{1}{4}\) Do \(\dfrac{12}{47}>\dfrac{1}{4}>\dfrac{19}{77}\) \(\Rightarrow\dfrac{12}{47}>\dfrac{19}{77}\) d) Ta có : A=\(\dfrac{13^{15}+1}{13^{16}+1}\) \(\Leftrightarrow\) 13A=\(\dfrac{13.\left(13^{15}+1\right)}{13^{16}+1}\) \(\Leftrightarrow\) 13A=\(\dfrac{13^{16}+13}{13^{16}+1}\) \(=\dfrac{13^{16}+1+12}{13^{16}+1}=\dfrac{13^{16}+1}{13^{16}+1}+\dfrac{12}{13^{16}+1}\)
\(=1+\dfrac{12}{13^{16}+1}\) B=\(\dfrac{13^{16}+1}{13^{17}+1}\) \(\Leftrightarrow\) 13B=\(\dfrac{13.\left(13^{16}+1\right)}{13^{17}+1}\)
\(\Leftrightarrow\) 13B=\(\dfrac{13^{17}+13}{13^{17}+1}=\dfrac{13^{17}+1+12}{13^{17}+1}\) \(=\dfrac{13^{17}+1}{13^{17}+1}+\dfrac{12}{13^{17}+1}\) \(=1+\dfrac{12}{13^{17}+1}\)
Do \(1+\dfrac{12}{13^{16}+1}.>1+\dfrac{12}{13^{17}+1}\) nên 13A>13B \(\Rightarrow\) A>B
d,
13A= 13.\(\dfrac{13^{15}+1}{13^{16}+1}\)=\(\)\(\dfrac{13^{16}+13}{13^{16}+1}\)=\(\dfrac{13^{16}+1+12}{13^{16}+1}\)= 1+\(\dfrac{12}{13^{16}+1}\)
13B=13.\(\dfrac{13^{16}+1}{13^{17}+1}\)=\(\dfrac{13^{17}+13}{13^{17}+1}\)=\(\dfrac{13^{17}+1+12}{13^{17}+1}\)=1+\(\dfrac{12}{13^{17}+1}\)
Vì \(\dfrac{12}{13^{16}+1}\)>\(\dfrac{12}{13^{17}+1}\)=> \(\dfrac{13^{15}+1}{13^{16}+1}\) > \(\dfrac{13^{16}+1}{13^{17}+1}\)
Mk làm câu d thôi nhé , các câu khác tự làm , thông cảm cho mk , nếu sai thôi nhé
Các câu dễ bạn tự làm nha:
Ta có:
\(\dfrac{a}{b}< 1\Rightarrow\dfrac{a+m}{b+m}< 1\left(m\in N\right)\)
\(B=\dfrac{13^{16}+1}{13^{17}+1}< 1\)
\(B< \dfrac{13^{16}+1+12}{13^{17}+1+12}\Rightarrow B< \dfrac{13^{16}+13}{13^{17}+13}\Rightarrow B< \dfrac{13\left(13^{15}+1\right)}{13\left(13^{16}+1\right)}\Rightarrow B< \dfrac{13^{15}+1}{13^{16}+1}=A\)
\(B< A\)
