\(4.3^{x-1}+2.3^{x+2}=4.3^6+2.3^9\)

\(3^{x-1}.\left(4+2.3^3\right)=3^6.\left(4+2.3^3\right)\)

\(\Leftrightarrow3^{x-1}=3^6\)

\(\Leftrightarrow x-1=6\)

\(\Leftrightarrow x=7\)

Vậy \(x=7\)

\(5^{x+4}-3.5^{x+3}=2.5^{11}\)

\(\Leftrightarrow5^{x+3}.\left(5-3\right)=2.5^{11}\)

\(\Leftrightarrow5^{x+3}.2=2.5^{11}\)

\(\Leftrightarrow5^{x+3}=5^{11}\)

⇔\(x+3=11\)

\(\Leftrightarrow x=8\)

Vậy \(x=8\)

\(11.6^{x-1}=11.6^{11}+2.6^{13}\)

\(\Rightarrow11.6^{x-1}=6^{11}.\left(11+2.36\right)\)

\(\Rightarrow11.6^{x-1}=6^{11}.83\)

B. 29/10

B

\(B.\dfrac{29}{10}\)

Ta có :      3/ 1 x 6 + 3/6 x 11 + 3/11 x 16 + ...+ 3/96 x 101 

= 3/5 x (  5/1 x 6 + 5/6 x 11 + 5/11 x 16 + ...+ 5/96 x 101 ) 

= 3/5 x  (  1 - 1/6 + 1/6 - 1/11 + 1/11 - 1/16 + ...+ 1/96 - 1/101 ) 

= 3/5 x  (  1 - 1/101 ) 

= 3/5 x    100/101 

= 60/101 

Tham khảo nha !!! 

Đặt A = \(\dfrac{3}{1.6}+\dfrac{3}{6.11}+...+\dfrac{3}{61.66}\)

=> \(\dfrac{5}{3}A=\dfrac{5}{1.6}+\dfrac{5}{6.11}+...+\dfrac{5}{61.66}\)

=> \(\dfrac{5}{3}A=1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...+\dfrac{1}{61}-\dfrac{1}{66}\)

=> \(\dfrac{5}{3}A=1-\dfrac{1}{66}=\dfrac{65}{66}\)

=> A = \(\dfrac{13}{22}\)

@nam nguyen

Đặt :

\(Â=\dfrac{3}{1.6}+\dfrac{3}{6.11}+...............+\dfrac{3}{61.66}\)

\(\Leftrightarrow A.\dfrac{5}{3}=\dfrac{5}{1.6}+\dfrac{5}{6.11}+..............+\dfrac{5}{61.66}\)

\(\Leftrightarrow A\dfrac{5}{3}=1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+.........+\dfrac{1}{61}-\dfrac{1}{66}\)

\(\Leftrightarrow A.\dfrac{5}{3}=1-\dfrac{1}{66}\)

\(\Leftrightarrow A.\dfrac{5}{3}=\dfrac{65}{66}\)

\(\Leftrightarrow A=\dfrac{13}{22}\)

Đặt \(A=\dfrac{3}{1.6}+\dfrac{3}{6.11}+\dfrac{3}{11.16}+...+\dfrac{3}{61.66}\)

\(A=3.\dfrac{1}{5}.\left(\dfrac{5}{1.6}+\dfrac{5}{6.11}+\dfrac{5}{11.16}+...+\dfrac{5}{61.66}\right)\)

\(A=\dfrac{3}{5}.\left(1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}+...+\dfrac{1}{61}-\dfrac{1}{66}\right)\)

\(A=\dfrac{3}{5}.\left(1-\dfrac{1}{66}\right)\)

\(A=\dfrac{3}{5}.\dfrac{65}{66}=\dfrac{13}{22}\)

rut 2 ra khoi mau so ,ben trong la 3/5+3/7+3/11

kết quả là 1/2

\(\frac{\frac{3}{5}+\frac{3}{7}-\frac{3}{11}}{\frac{6}{5}+\frac{6}{7}-\frac{6}{11}}=\frac{3.\left(\frac{1}{5}+\frac{1}{7}-\frac{1}{11}\right)}{6.\left(\frac{1}{5}+\frac{1}{7}-\frac{1}{11}\right)}\)\(=\frac{1}{2}\).

Giải:

\(11\dfrac{3}{4}-\left(6\dfrac{5}{6}-4\dfrac{1}{2}\right)+1\dfrac{2}{3}\) 

\(=\dfrac{47}{4}-\left(\dfrac{41}{6}-\dfrac{9}{2}\right)+\dfrac{5}{3}\) 

\(=\dfrac{47}{4}-\dfrac{41}{6}+\dfrac{9}{2}+\dfrac{5}{3}\) 

\(=\dfrac{141}{12}-\dfrac{82}{12}+\dfrac{54}{12}+\dfrac{20}{12}\) 

\(=\dfrac{141-82+54+20}{12}\) 

\(=\dfrac{133}{12}\) 

Chúc bạn học tốt!

=133/12

a: \(=\dfrac{-3-5-7}{4}=\dfrac{-15}{4}\)

b: \(=\dfrac{-6-5-2+6}{11}=\dfrac{-7}{11}\)

L: \(\dfrac{7}{6}\) +\(\dfrac{8}{6}\) = \(\dfrac{15}{6}\)

T: \(\dfrac{1}{11}\) + \(\dfrac{7}{11}\) + \(\dfrac{9}{11}\) = \(\dfrac{17}{11}\)

Ạ: \(\dfrac{4}{11}\) + \(\dfrac{2}{11}\) = \(\dfrac{6}{11}\)

Đ: \(\dfrac{3}{6}\) + \(\dfrac{1}{6}\) + \(\dfrac{7}{6}\) = \(\dfrac{11}{6}\)

À: \(\dfrac{3}{11}\) + \(\dfrac{9}{11}\) = \(\dfrac{12}{11}\)

ĐÀ LẠT

\(A=\dfrac{5}{11}.\dfrac{5}{7}+\dfrac{5}{11}.\dfrac{2}{7}+\dfrac{6}{11}=\dfrac{5}{11}\left(\dfrac{5}{7}+\dfrac{2}{7}\right)+\dfrac{6}{11}=\dfrac{5}{11}.1+\dfrac{6}{11}=\dfrac{5}{11}+\dfrac{6}{11}=\dfrac{11}{11}=1\)

\(B=\dfrac{3}{13}.\dfrac{6}{11}+\dfrac{3}{13}.\dfrac{9}{11}-\dfrac{3}{13}.\dfrac{4}{11}=\dfrac{3}{13}\left(\dfrac{6}{11}+\dfrac{9}{11}-\dfrac{4}{11}\right)=\dfrac{3}{13}.1=\dfrac{3}{13}\)

\(C=\left(\dfrac{12}{16}-\dfrac{31}{22}+\dfrac{14}{91}\right)\left(\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{1}{6}\right)=\left(\dfrac{12}{16}-\dfrac{31}{22}+\dfrac{14}{91}\right)\left(\dfrac{3}{6}-\dfrac{2}{6}-\dfrac{1}{6}\right)=\left(\dfrac{12}{16}-\dfrac{31}{22}+\dfrac{14}{91}\right).0=0\)

Phương pháp giải:

- Tính giá trị của mỗi vế.

- So sánh rồi điền dấu thích hợp vào chỗ trống.

Lời giải chi tiết:

6 + 8 = 8 + 6

6 + 6 < 6 + 8

9 + 8 – 5 > 11

6 + 7 – 3 < 11  

dung roi do