Question

[Cô Bé Xinh Xắn]

So sánh:

a, \(\frac{27}{82}\)với \(\frac{26}{75}\)

b, \(\frac{-49}{78}\)với \(\frac{64}{-95}\)

c, \(\frac{2525}{2929}\)với \(\frac{217}{245}\)

d, A= \(\frac{3^{10}+1}{3^9+1}\) với B= \(\frac{3^9+1}{3^8+1}\)

e, P= \(\frac{5^4.107-53}{5^3.107+54}\) với Q= \(135.\frac{269-133}{134.269+135}\)

Answer 1

[l҉o҉n҉g҉ d҉z҉]

Ta có : \(A=\frac{3^{10}+1}{3^9+1}\) => \(A.\frac{1}{3}=\frac{3^{10}+1}{3^{10}+3}=\frac{\left(3^{10}+3\right)-2}{3^{10}+3}=1-\frac{2}{3^{10}+3}\)

           \(B.\frac{1}{3}=\frac{3^9+1}{3^8+1}\Rightarrow B.\frac{1}{3}=\frac{3^9+1}{3^9+3}=\frac{\left(3^9+3\right)-2}{3^9+3}=1-\frac{2}{3^9+3}\)

Vì : \(\frac{2}{3^{10}+3}< \frac{2}{3^9+3}\) nên \(A>B\)

Answer 2

[vu tien dat]

\(a,\frac{27}{82}< \frac{27}{83}=\frac{1}{3};\frac{26}{75}>\frac{25}{75}=\frac{1}{3}\)

nên\(\frac{27}{82}< \frac{26}{75}\)

\(b,\frac{49}{78}< \frac{52}{78}=\frac{2}{3};\frac{64}{95}>\frac{64}{96}=\frac{2}{3}\)

nên\(\frac{49}{78}< \frac{64}{95}\Rightarrow\frac{-49}{78}>\frac{64}{-95}\)

c, Rút gọn:\(\frac{2525}{2929}=\frac{25}{29};\frac{217}{245}=\frac{31}{35}\)

Ta có:\(1-\frac{25}{29}=\frac{4}{29};1-\frac{31}{35}=\frac{4}{35}\Rightarrow1-\frac{25}{29}>1-\frac{31}{35}\)

\(\Rightarrow\frac{25}{29}< \frac{31}{35}\)hay\(\frac{2525}{2929}< \frac{217}{245}\)

\(d,A=\frac{3^{10}+1}{3^9+1}=1+\frac{3}{3^9+1}\);\(B=\frac{3^9+1}{3^8+1}=1+\frac{3}{3^8+1}\)

Dễ dàng nhận thấy \(\frac{3}{3^9+1}< \frac{3}{3^8+1}\Rightarrow A< B\)

Xin lỗi bạn e, mk ko làm được. Chúc bạn học tốt