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\(x+2x+3x+...+9x=459-3^2\)
\(\Rightarrow9x+\left(1+2+3+...+9\right)=450\)
\(\Rightarrow9x+\frac{\left[\left(9+1\right).9\right]}{2}=450\)
\(\Rightarrow9x+45=450\)
\(\Rightarrow9x=450-45\)
\(\Rightarrow x=\frac{450-45}{9}=\frac{405}{9}=45\)
a. \(\frac{1}{1.2}+...+\frac{1}{x.\left(x+1\right)}=99\)
\(\Rightarrow\frac{1}{1}-\frac{1}{2}+...+\frac{1}{x}-\frac{1}{x+1}=99\)
\(\Rightarrow1-\frac{1}{x+1}=99\)
\(\Rightarrow\frac{1}{x+1}=1-99=-98\)
\(\Rightarrow x=\frac{1}{-98}-1\)
\(\Rightarrow x=-\frac{99}{98}\)
P/s : Bạn ơi đề sai, x sai hay mk sai ạ???
A, 1/(1.2)+...+1/[x(x+1)]=99
=>1-1/2+...+1/x+1/(x-1)=99
=>1-1/(x-1)=99
=>1/(x-1)=-98
=>1/(x-1)=-98/1
=>1.(-98)=(x-1).1(tích chéo)
=>x-1=-98
=>x=-97
a) 33x+1 . 5 = 10935
=> 33x . 3 . 5 = 10935
=> 27x . 3 . 5 = 10935
=> 27x = 729
=> 27x = 272
=> x = 2
b) 25x + 1 . 3 = 6144
=> 25x . 2 . 3 = 6144
=> 32x . 6 = 6144
=> 32x = 1024
=> 32x = 322
=> x = 2
c) (2x + 3)4 = 625
=> (2x + 3)4 = (\(\pm\)5)4
=> \(\orbr{\begin{cases}2x+3=5\\2x+3=-5\end{cases}}\Rightarrow\orbr{\begin{cases}x=1\\x=-4\end{cases}}\)
d) (3x + 1)3 = 343
=> (3x + 1)3 = 73
=> 3x + 1 = 7 => 3x = 6 => x = 2
Mình giải câu b) bài 1: \(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+...+\left(x+100\right)=5750\)
\(\Leftrightarrow\left(x+x+x+...+x\right)+\left(1+2+3+...+100\right)\) (100 số hạng)
\(\Leftrightarrow100x+5050=5750\Leftrightarrow100x=5750-5050=700\)
Ta có: \(100x=700\Leftrightarrow x=7\)
-\(x\) + 30% \(\times\) \(x\) = -1,3
-\(x\) + 0,3\(\times\) \(x\) = -1,3
\(x\times\) ( 1 - 0,3) = -1,3
\(x\) \(\times\)(- 0,7) = -1,3
\(x\) = (-1,3) : (-0,7)
\(x\) = \(\dfrac{13}{7}\)
\(3^{3x+1}.5=10935\)
\(\Rightarrow3^{3x+1}=10935:5\)
\(\Rightarrow3^{3x+1}=2187\)
\(\Rightarrow3^{3x+1}=3^7\)
\(\Rightarrow3x+1=7\)
\(\Rightarrow3x=6\)
\(\Rightarrow x=2\)
\(2^{5x+1}.3=6144\)
\(\Rightarrow2^{5x+1}=6144:3\)
\(\Rightarrow2^{5x+1}=2048\)
\(\Rightarrow2^{5x+1}=2^{11}\)
\(\Rightarrow5x+1=11\)
\(\Rightarrow5x=10\)
\(\Rightarrow x=2\)
1) 33.x+1.5=10935
33.x+1 = 10935 : 5
33.x+1 = 2187
Mà 2187 = 37
=> 33.x+1 = 37
=> 3.x + 1 = 7
=> 7 = 3.2+1 = 6 +1 = 7
=> 33.2+1 . 5 = 10935
2) 25.x+1.3=6144
25.x+1 = 6144 : 3
25.x+1 = 2048
=> 2048 = 25.x+1
Mà 2048 = 211
=> 211 = 25.x+1
=> 5.x + 1 = 11
=> 11 = 5.2+1 = 10 +1 = 11
=> 25.2+1 . 5 = 10935