\(\frac{3^4.2-3^6}{3^4.17+4.3^4}\), tính nhanh nhé.
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\(\frac{x+5}{3}=\frac{5}{9}\)
=> ( x + 5 ) x 9 = 3 x 5
=> x + 5 = \(\frac{3\cdot5}{9}\)
=> x + 5 = \(\frac{5}{3}\)
=> x = \(\frac{-10}{3}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
4.2: cho A = -12,7.32,6 + 12,7.2,6 + 2,7.17,2. Giá trị của biểu thức A là:
(A) -300 (B) -200 (C) 200 (D) 200
4.3: Cho a = -6,b=3,c= -2
tính: |a+b-c|; |a-b+c|; |a-b-c|
5.2: số \(x^{14}\)là kết quả của phép toán
(A) \(x^{14}:x\) (B) \(x^7.x^2\) (C) \(x^8.x^6\) (D) \(x^{14}.x\)
5.4 tìm số nguyên n lớn nhất sao cho \(n^{150}< 5^{225}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{4k}{4k^4+1}=\frac{4k}{4k^4+4k^2+1-4k^2}=\frac{4k}{\left(2k^2+1\right)^2-\left(2k\right)^2}=\frac{4k}{\left(2k^2+2k+1\right)\left(2k^2-2k+1\right)}=\frac{1}{2k^2-2k+1}-\frac{1}{2k^2+2k+1}\)
\(=\frac{1}{2k\left(k-1\right)+1}-\frac{1}{2k\left(k+1\right)+1}\)
\(A=\frac{1}{1}-\frac{1}{5}+\frac{1}{5}-\frac{1}{13}+...+\frac{1}{2k\left(k-1\right)+1}-\frac{1}{2k\left(k+1\right)+1}\)
\(=1-\frac{1}{2k\left(k+1\right)+1}=...\)
![](https://rs.olm.vn/images/avt/0.png?1311)
câu 2 là 3<1+1/2+1/3+1/4+...+1/62+1/63<6 nhé
mk ghi nhầm đề baif
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có: \(4n^4+1=\left(4n^4+4n^2+1\right)-4n^2=\left(2n^2+2n+1\right)\left(2n^2-2n+1\right)\)
\(\frac{4n}{4n^4+1}=\frac{\left(2n^2+2n+1\right)-\left(2n^2-2n+1\right)}{\left(2n^2-2n+1\right)\left(2n^2+2n+1\right)}=\frac{1}{2n^2-2n+1}-\frac{1}{2n^2+2n+1}\)
Thay vào ta có:
\(\frac{4.1}{4.1^4+1}+\frac{4.2}{4.2^2+1}+...+\frac{4n}{4n^4+1}=\frac{220}{221}\)
\(\Leftrightarrow1-\frac{1}{5}+\frac{1}{5}-\frac{1}{13}+...+\frac{1}{2n^2-2n+1}-\frac{1}{2n^2+2n+1}=\frac{220}{221}\)
\(\Leftrightarrow1-\frac{1}{2n^2+2n+1}=\frac{220}{221}\)
\(\Leftrightarrow\frac{2n^2+2n}{2n^2+2n+1}=\frac{220}{221}\Rightarrow n=10\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a, \(\left(\frac{1}{2}-\frac{1}{3}\right)\cdot6^x+6^{x+2}=6^{10}+6^7\)
\(\Leftrightarrow\frac{1}{6}\cdot6^x+6^x\cdot6^2=6^{10}+6^7\)
\(\Leftrightarrow6^{x-1}\left(1+6^3\right)=6^7\left(6^3+1\right)\)
\(\Leftrightarrow6^{x-1}=6^7\Leftrightarrow x-1=7\)
\(\Leftrightarrow x=8\)
b, \(\left(\frac{1}{2}-\frac{1}{6}\right)\cdot3^{x+4}-4\cdot3^x=3^{16}-4\cdot3^{13}\)
\(\Leftrightarrow\frac{1}{3}\cdot3^{x+4}-4\cdot3^x=3^{13}\left(3^3-4\right)\)
\(\Leftrightarrow3^x\cdot3^3-4\cdot3^x=3^{13}\left(3^3-4\right)\)
\(\Leftrightarrow3^x\left(3^3-4\right)=3^{13}\left(3^3-4\right)\)
\(\Leftrightarrow3^x=3^{13}\Leftrightarrow x=13\)
a. x=8
b. x=13
còn cách tính thì mình quên rồi vì minh học cái này lâu lắm rồi ko nhớ đc.
![](https://rs.olm.vn/images/avt/0.png?1311)
a)1/9.27^n=3^n
3^n=3^n
=>n={0;1;2;3...}
Tích nha ^_^ !!!
\(\frac{3^4.2-3^6}{3^4.17+4.3^4}\)
\(=\frac{3^4.\left(2-9\right)}{3^4.\left(17+4\right)}\)
\(=\frac{-7}{21}=-\frac{1}{3}\)
HT
\(\frac{3^4.2-3^6}{3^4.17+\left(2-9\right)}\)
\(=\frac{3^4.\left(2+9\right)}{3^4.\left(17+4\right)}\)
\(=\frac{-7}{21}=-\frac{1}{3}\)
_HT_