Bài 1:
1: \(\left(x+7\right)-25=13\)
=>x+7=25+13=38
=>x=38-7=31
2: \(87-\left(73-x\right)=20\)
=>73-x=87-20=67
=>x=73-67=6
3: \(x-105:21=15\)
=>x-5=15
=>x=15+5=20
4: \(15+\left(x+2\right)^2:3=18\)
=>\(\left(x+2\right)^2:3=18-15=3\)
=>\(\left(x+2\right)^2=3\cdot3=9\)
=>\(\left[{}\begin{matrix}x+2=3\\x+2=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\left(nhận\right)\\x=-5\left(loại\right)\end{matrix}\right.\)
5: \(20-2\left(x-1\right)^2=2\)
=>\(2\left(x-1\right)^2=20-2=18\)
=>\(\left(x-1\right)^2=9\)
=>\(\left[{}\begin{matrix}x-1=3\\x-1=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\left(nhận\right)\\x=-2\left(loại\right)\end{matrix}\right.\)
6: \(3^{x-1}+3^x+3^{x+1}=39\)
=>\(3^x\cdot\dfrac{1}{3}+3^x+3^x\cdot3=39\)
=>\(3^x\cdot\left(\dfrac{1}{3}+4\right)=39\)
=>\(3^x=39:\dfrac{13}{3}=39\cdot\dfrac{3}{13}=3\cdot3=3^2\)
=>x=2
Bài 2:
1: \(x\inƯ\left(18\right)\)
=>\(x\in\left\{1;2;3;6;9;18\right\}\)
mà \(x\in B\left(4\right)\)
nên \(x\in\varnothing\)
2: \(x\inƯ\left(20\right)\)
=>\(x\in\left\{1;2;4;5;10;20\right\}\)
mà \(x\in B\left(2\right)\)
nên \(x\in\left\{2;4;10;20\right\}\)
3: \(x\in B\left(12\right)\)
=>\(x\in\left\{0;12;24;36;48;60;72;84;96;108;...\right\}\)
mà 30<=x<=100
nên \(x\in\left\{36;48;60;72;84;96\right\}\)
4: \(x\inƯ\left(150\right)\)
=>\(x\in\left\{1;2;3;5;6;10;15;25;30;50;75;150\right\}\)
mà x<=50
nên \(x\in\left\{1;2;3;5;6;10;15;25;30;50\right\}\)
