\(a,\frac{x+1}{65}+\frac{x+2}{64}=\frac{x+3}{63}+\frac{x+4}{62}\)

\(\Rightarrow\left[\frac{x+1}{65}+1\right]+\left[\frac{x+2}{64}+1\right]=\left[\frac{x+3}{63}+1\right]+\left[\frac{x+4}{62}+1\right]\)

\(\Rightarrow\frac{x+1+65}{65}+\frac{x+2+64}{64}=\frac{x+3+63}{63}+\frac{x+4+62}{62}\)

\(\Rightarrow\frac{x+66}{65}+\frac{x+66}{64}=\frac{x+66}{63}+\frac{x+66}{62}\)

\(\Rightarrow\frac{x+66}{65}+\frac{x+66}{64}=\frac{x+66}{63}+\frac{x+66}{62}=0\)

\(\Rightarrow\left[x+66\right]\left[\frac{1}{65}+\frac{1}{64}-\frac{1}{63}+\frac{1}{62}\right]=0\)

Mà \(\frac{1}{65}+\frac{1}{64}-\frac{1}{63}+\frac{1}{62}\ne0\)

\(\Rightarrow x+66=0\)

\(\Rightarrow x=0-66=-66\)

Auto làm nốt câu b

a,  Cộng cả 2 vế với 2 

Ta có \(\frac{x+1}{64}+\frac{x+2}{63}+2=\frac{x+3}{62}+\frac{x+4}{61}+2\)

\(\left(\frac{x+1}{64}+\frac{64}{64}\right)+\left(\frac{x+2}{63}+\frac{63}{63}\right)=\left(\frac{x+3}{62}+\frac{62}{62}\right)+\left(\frac{x+4}{61}+\frac{61}{61}\right)\)

=>  \(\frac{x+65}{64}+\frac{x+65}{63}=\frac{x+65}{62}+\frac{x+65}{61}\)\(\)

=> \(\frac{x+65}{64}+\frac{x+65}{63}-\frac{x+65}{62}-\frac{x+65}{61}=0\)

=> \(\left(x+65\right)\left(\frac{1}{64}+\frac{1}{63}-\frac{1}{62}-\frac{1}{61}\right)=0\)

Do \(\frac{1}{64}+\frac{1}{63}-\frac{1}{62}-\frac{1}{61}\ne0\)=> \(x+65=0\)

=> \(x=-65\)

b ,  Lm tương tự như Câu a

Chúc bn hok tốt

a) \(\frac{x+1}{65}+\frac{x+2}{64}=\frac{x+3}{63}+\frac{x+4}{62}\)

\(\Leftrightarrow\frac{x+1}{65}+\frac{x+2}{64}+2=\frac{x+3}{63}+\frac{x+4}{62}+2\)

\(\Leftrightarrow\left(\frac{x+1}{65}+1\right)+\left(\frac{x+2}{64}+1\right)=\left(\frac{x+3}{63}+1\right)+\left(\frac{x+4}{62}+1\right)\)

\(\Leftrightarrow\frac{x+1+65}{65}+\frac{x+2+64}{64}=\frac{x+3+63}{63}+\frac{x+4+62}{62}\)

\(\Leftrightarrow\frac{x+66}{65}+\frac{x+66}{64}=\frac{x+66}{63}+\frac{x+66}{62}\)

\(\Leftrightarrow\frac{x+66}{65}+\frac{x+66}{64}-\frac{x+66}{63}-\frac{x+66}{62}=0\)

\(\Leftrightarrow\left(x+66\right)\left(\frac{1}{65}+\frac{1}{64}-\frac{1}{63}-\frac{1}{62}\right)=0\)

\(\Leftrightarrow x+66=0\)

\(\Leftrightarrow x=-66\)

CÂu b) làm tương tự:

- Trừ 3 cho hai vế ( câu a) mk cộng 2 cho hai vế)

- Tách -3 = -1-1-1 rồi kết hợp với mỗi hạng tử

CỐ LÊN NHÉ

NẾU bạn KHÔNG HIỂU thì câu b) mik sẽ làm kĩ càng và rõ ràng hơn cho bạn hiểu

\(\frac{1}{4}\cdot\frac{2}{6}\cdot\frac{3}{8}\cdot......\cdot\frac{31}{64}=2^x\)

\(\Leftrightarrow\frac{1\cdot2\cdot3\cdot....\cdot31}{4\cdot6\cdot8\cdot....\cdot64}=2^x\)

\(\Leftrightarrow\frac{1\cdot2\cdot3\cdot....\cdot31}{\left(2\cdot2\right)\cdot\left(3\cdot2\right)\cdot\left(4\cdot2\right)\cdot.....\cdot\left(2\cdot32\right)}=2^x\)

\(\Leftrightarrow\frac{1\cdot2\cdot3\cdot...\cdot31}{\left(2\cdot2\cdot2\cdot....\cdot2\right)\left(1\cdot2\cdot3\cdot.....\cdot31\right)\cdot32}=2^x\)

\(\Leftrightarrow\frac{1}{2^{31}.2^5}=2^x\)

\(\Leftrightarrow\frac{1}{2^{36}}=2^x\)

\(\Rightarrow x=-36\)

1/4 . 2/6 . 3/8 . ... .30/62 .31/64 = 2^x

(1/2 . 1/2).(2/3 . 1/2).(3/4 . 1/2). ... .(30/31 . 1/2).(31/32 . 1/2) = 2^x

(1/2.1/2. ... .1/2).(1/2 . 2/3 . 3/4. ... .30/31 . 31/32) = 2^x

   (31 số 1/2) 

(1/2)^31.  = 2^x

=> 0=x+36

      x=0-36

      x=-36

Vậy x=-36

Theo mk nghĩ,mk làm đúng nha .Tk cho mk

Để mk sửa phần này một chút

\((\frac{1}{2})^{31}\cdot\frac{1\cdot2\cdot3.....30\cdot31}{2\cdot3\cdot4.....31\cdot32}=2^x\)

\(\frac{1^{31}}{2^{31}}\cdot\frac{1}{32}=2^x\)

\(\frac{1}{2^{31}}\cdot\frac{1}{2^5}=2^x\)

\(\frac{1}{2^{36}}=2^x\)

\(1=2^x\cdot2^{36}\)

\(2^0=2^x+36\)

Rồi bn tự suy luận nha

\(\frac{1}{4}.\frac{2}{6}.\frac{3}{8}.........................\frac{31}{64}=\frac{1}{2^x}\)

Có 31 thừa số

\(\Leftrightarrow\left(\frac{1}{2}.\frac{1}{2}\right).\left(\frac{1}{2}.\frac{2}{3}\right)...................\left(\frac{1}{2}.\frac{31}{32}\right)=\frac{1}{2^x}\)

\(\Leftrightarrow\left(\frac{1}{2}.\frac{1}{2}...............\frac{1}{2}\right).\left(\frac{1}{2}.\frac{2}{3}...............\frac{31}{32}\right)=\frac{1}{2^x}\)

Có 31 thừa số                                            Có 31 thừa số

\(\Leftrightarrow\frac{1}{2^{31}}.\frac{1.2....................31}{2.3..............32}=\frac{1}{2^x}\)

\(\Leftrightarrow\frac{1}{2^{31}}.\frac{1}{32}=\frac{1}{2^x}\)

\(\Leftrightarrow\frac{1}{2^{31}}.\frac{1}{2^5}=\frac{1}{2^x}\)

\(\Leftrightarrow\frac{1}{2^{36}}=\frac{1}{2^x}\)

\(\Leftrightarrow x=36\)

Vậy x=36

Chúc bạn học tốt

a) \(\left|2-\frac{3}{2}x\right|-4=x+2\)

=> \(\left|2-\frac{3}{2}x\right|=x+2+4\)

=> \(\left|2-\frac{3}{2}x\right|=x+6\)

ĐKXĐ : \(x+6\ge0\) => \(x\ge-6\)

Ta có: \(\left|2-\frac{3}{2}x\right|=x+6\)

=> \(\orbr{\begin{cases}2-\frac{3}{2}x=x+6\\2-\frac{3}{2}x=-x-6\end{cases}}\)

=> \(\orbr{\begin{cases}2-6=x+\frac{3}{2}x\\2+6=-x+\frac{3}{2}x\end{cases}}\)

=> \(\orbr{\begin{cases}\frac{5}{2}x=-4\\\frac{1}{2}x=8\end{cases}}\)

=> \(\orbr{\begin{cases}x=-\frac{8}{5}\\x=16\end{cases}}\) (tm)

b) \(\left(4x-1\right)^{30}=\left(4x-1\right)^{20}\)

=> \(\left(4x-1\right)^{30}-\left(4x-1\right)^{20}=0\)

=> \(\left(4x-1\right)^{20}.\left[\left(4x-1\right)^{10}-1\right]=0\)

=> \(\orbr{\begin{cases}\left(4x-1\right)^{20}=0\\\left(4x-1\right)^{10}-1=0\end{cases}}\)

=> \(\orbr{\begin{cases}4x-1=0\\\left(4x-1\right)^{10}=1\end{cases}}\)

=> \(\orbr{\begin{cases}4x=1\\4x-1=\pm1\end{cases}}\)

=> x = 1/4

hoặc x = 0 hoặc x = 1/2

Ta có: \(\frac{1}{2.2}.\frac{2}{2.3}.\frac{3}{2.4}.\frac{4}{2.5}.\frac{5}{2.6}.......\frac{30}{2.31}.\frac{31}{64}=4^x\)

\(\frac{1}{2^{30}.64}=4^x\Leftrightarrow4^x.2^{30}.2^6=1\)

\(\Leftrightarrow2^{2x+36}2^0\)

\(\Leftrightarrow2x+36=0\)

\(\Leftrightarrow2x=-36\)

\(\Leftrightarrow x=-18\)

Vậy ........

$4^x.64=1$\(\frac{1}{4}.\frac{2}{6}.\frac{3}{8}.\frac{4}{10}.\frac{5}{12}.....\frac{30}{62}.\frac{31}{64}=4^x\)

\(\Leftrightarrow\frac{1}{2.2}.\frac{2}{2.3}.\frac{3}{2.4}.\frac{4}{2.5}.\frac{5}{2.6}.....\frac{30}{2.31}.\frac{31}{2.32}=4^x\)

\(\Leftrightarrow\frac{1}{2}\left(\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}.\frac{5}{6}.....\frac{30}{31}.\frac{31}{32}\right)=4^x\)

\(\Leftrightarrow\frac{1}{2}.\frac{1.2.3.4.5.....30.31}{2.3.4.5.6.....31.32}=4^x\)

\(\Leftrightarrow\frac{1}{2}.\frac{1}{32}=4^x\)

\(\Leftrightarrow4^x=\frac{1}{64}\)

\(\Leftrightarrow4^x.64=1\)

\(\Leftrightarrow4^x.4^3=1\Leftrightarrow4^{x+3}=4^0\Leftrightarrow x+3=0\Leftrightarrow x=-3\)

Vậy x = -3

\(\frac{1}{4}.\frac{2}{6}.\frac{3}{8}.\frac{4}{10}.\frac{5}{12}...\frac{30}{62}.\frac{31}{64}=4^x\)

\(\Leftrightarrow\frac{1}{2.2}.\frac{2}{2.3}.\frac{3}{2.4}.\frac{4}{2.5}.\frac{5}{2.6}...\frac{30}{2.31}.\frac{31}{2.32}=4^x\)

\(\Leftrightarrow\frac{1.2.3.4.5...30.31}{2.2.2.3.2.4.2.5.2.6...2.31.2.32}=4^x\)

\(\Leftrightarrow\frac{2.3.4.5...30.31}{2^{31}.32.\left(2.3.4.5...31\right)}=4^x\)

\(\Leftrightarrow\frac{1}{2^{31}.2^5}=4^x\)

\(\Leftrightarrow\frac{1}{2^{36}}=4^x\)

\(\Leftrightarrow\frac{1}{4^{18}}=4^x\)

\(\Leftrightarrow x=-18\)

Câu b thôi các bạn nhé, câu a mình ko cần nx với cả mình ghi sai dữ liệu câu a r

a, \(\frac{1}{4}\cdot\frac{2}{6}\cdot\frac{3}{8}\cdot\frac{4}{10}\cdot...\cdot\frac{30}{62}\cdot\frac{31}{64}=2x\)

\(\Leftrightarrow\frac{1\cdot2\cdot3\cdot4\cdot...\cdot30\cdot31}{4\cdot6\cdot8\cdot10\cdot...\cdot62\cdot64}=2x\)

\(\Leftrightarrow\frac{1\cdot2\cdot3\cdot4\cdot...\cdot30\cdot31}{2\cdot2\cdot3\cdot2\cdot4\cdot2\cdot5\cdot2\cdot....\cdot31\cdot2\cdot32\cdot2}=2x\)

\(\Leftrightarrow\frac{1}{2\cdot2\cdot2\cdot2\cdot....\cdot2\cdot2\cdot32}=2x\)

Có  : (31 - 1) : 1 + 1 = 31 (thừa số 2) 

\(\Rightarrow\frac{1}{2^{31}.32}=2x\)

\(\Rightarrow x=\frac{1}{2^{31}.32}\div2\)

b, \(\left(x-1\right)^{x+2}=\left(x-1\right)^{x+4}\)

\(\Leftrightarrow x+1=x+4\)

\(\Leftrightarrow0=3\text{ (vô lý) }\)

Tìm x biết :             \(\frac{1}{4}.\frac{2}{6}.\frac{3}{8}.\frac{4}{10}.\frac{5}{12}...\frac{30}{62}.\frac{31}{64}=2x\) 

 Biến đổi mẫu thức của vế trái :     \(\frac{1}{2.2}.\frac{2}{2.3}.\frac{3}{2.4}.\frac{4}{2.5}.\frac{5}{2.6}...\frac{30}{2.31}.\frac{31}{2.32}=2x\)   Giản ước vế trái đực :

                                               \(\frac{1}{2}.\frac{1}{2}.\frac{1}{2}.\frac{1}{2}.\frac{1}{2}...\frac{1}{2}.\frac{1}{2.32}=2x\)        (*)   

                                                  \(\Leftrightarrow\frac{1}{2^{36}}=2x\Leftrightarrow x=\frac{1}{2^{37}}\)  

\(\frac{1.2.3....31}{2^{30}.\left(2.3....31\right).32}=\frac{1}{2^{31}.32}=\frac{1}{2^{36}}=2^{-36}=2^x\)

Vậy x=-36

Hok tốt