Đk: x khác 0;

pt \(\Leftrightarrow-9\cdot2^{\frac{1}{x}}-5\cdot2^{\frac{1}{x}}\cdot3^{\frac{1}{x}}+4\cdot3^{\frac{2}{x}}=0\)

\(\Leftrightarrow4\cdot\left(3^{\frac{1}{x}}\right)^2-5\cdot2^{\frac{1}{x}}\cdot3^{\frac{1}{x}}-9\cdot2^{\frac{1}{x}}=0\)

xem pt trên là pt bậc hai ẩn 3^1/x, ta có: \(\Delta=\left(5\cdot2^{\frac{1}{x}}\right)^2-4\cdot4\cdot\left(-9\cdot2^{\frac{2}{x}}\right)=169\cdot2^{\frac{1}{x}}\)

\(3^{\frac{1}{x}}=\frac{5\cdot2^{\frac{1}{x}}-13\cdot2^{\frac{1}{x}}}{2\cdot4}=-2^{\frac{1}{x}}\) (loại)

\(3^{\frac{1}{x}}=\frac{5\cdot2^{\frac{1}{x}}+13\cdot2^{\frac{1}{x}}}{2\cdot4}=\frac{9}{4}\cdot2^{\frac{1}{x}}\Leftrightarrow3^{\frac{1}{x}-2}=2^{\frac{1}{x}-2}\Leftrightarrow\frac{1}{x}-2=0\Leftrightarrow x=\frac{1}{2}\)

B cho mình hỏi hình như thiếu dấu ngoặc

x=2

tick cho mình nha 

\(\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{8.9.10}\right).x=\frac{22}{45}\)  vậy

\(\frac{11}{45}.x=\frac{22}{45}\)

\(x=\frac{22}{45}\div\frac{11}{45}=2\)

vậy suy ra x =2

mình chắc chắn 100% luôn đó, cái này ở trong violympic toán 7 vòng 12 phải ko
 

\(\frac{5^{102}\cdot9^{1000}}{3^{2018}\cdot25^{50}}=\frac{5^{102}\cdot3^{2000}}{3^{2018}\cdot5^{100}}=\frac{5^2}{3^{18}}\)

X=2 nhé bạn.....đúng đó, vòng 12 mk 300 mà cx gặp câu này!!! Tick nha

Trước hết ta thực hiện biểu thức trong ngoặc:

\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{8.9.10}\)

\(=\frac{1}{2}\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{8.9.10}\right)\)

\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{8.9}-\frac{1}{9.10}\right)\)

\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{9.10}\right)\)

\(=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{90}\right)\)

\(=\frac{1}{2}.\frac{22}{45}\) \(=\frac{11}{45}\)

\(\Rightarrow\frac{11}{45}\) \(.x=\frac{22}{45}\)

\(\Rightarrow x=\frac{22}{45}:\frac{11}{45}\)

\(\Rightarrow x=2\)

\(\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{8.9.10}\right).x=\frac{23}{45}\)

\(\frac{1}{2}.\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{8.9.10}\right).x=\frac{23}{45}\)

\(\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{8.9}-\frac{1}{9.10}\right).x=\frac{23}{45}\)

\(\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{9.10}\right).x=\frac{23}{45}\)

\(\frac{1}{2}.\frac{22}{45}.x=\frac{23}{45}\)

         \(\frac{11}{45}.x=\frac{23}{45}\)

                  \(x=\frac{23}{45}:\frac{11}{45}\)

                 \(x=\frac{23}{11}\)

Gọi A=(1/1.2.3+ 1/2.3.4 +...+ 1/8.9.10) .x=23/45

    2A=3-1/1.2.3+ 4–2/2.3.4+ 5–4/3.4.5+ ... + 10–8/8.9.10

    2A=1/2 —1/2.3+ 1/2.3 — 1/3.4+ 1/3.4– 1/4.5 +...+1/8.9–1/9.10=1/2–1/9.10=44/90

     A=44/90 : 2=22/90

     x=23/45:A= 23/45 : 22/90=23/11= 2 1/1( hỗn số)

Nhầm đáp án là 2 1/11 nhé