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a: \(\Leftrightarrow x-3\inƯ\left(21\right)\)
\(\Leftrightarrow x-3\in\left\{-3;-1;1;3;7;21\right\}\)
hay \(x\in\left\{0;2;4;6;10;24\right\}\)
b: \(\Leftrightarrow x-1\in\left\{1;-1;17\right\}\)
hay \(x\in\left\{2;0;18\right\}\)
c: \(\Leftrightarrow2x-1+4⋮2x-1\)
\(\Leftrightarrow2x-1\in\left\{1;-1\right\}\)
hay \(x\in\left\{1;0\right\}\)
d: \(\Leftrightarrow x^2+x+3⋮x+1\)
\(\Leftrightarrow x+1\inƯ\left(3\right)\)
\(\Leftrightarrow x+1\in\left\{1;3\right\}\)
hay \(x\in\left\{0;2\right\}\)
b,
(x-2)3=-125
(x-2)3=(-5)3
suy ra x-2=-5
x=-5+2
x=-3
vậy x=-3
c, làm tương tự ý b
a: \(x\in\left\{1;2;3;6;9;18\right\}\)
mà \(x\in B\left(4\right)\)
nên \(x\in\varnothing\)
b: \(x\in\left\{1;2;3;4;6;9;12;18;36\right\}\)
mà x>=12
nên \(x\in\left\{12;18;36\right\}\)
c: \(x\in\left\{0;12;24;36;48;60;72;84;96;108;...\right\}\)
mà 30<=x<=100
nên \(x\in\left\{36;48;60;72;84;96\right\}\)
d: \(x\inƯC\left(28;21\right)\)
\(\Leftrightarrow x\inƯ\left(7\right)\)
hay \(x\in\left\{1;7\right\}\)
a)\(x\in\left\{3;6;9;18\right\}\)
b)\(x\in\left\{12;18;36\right\}\)
c)\(x\in\left\{36;48;60;72;84;96\right\}\)
d)\(x\in\left\{7;1\right\}\)
câu a: x=18,6,3,9
câu b: x=12,18,36
câu c: x=60
câu d: x=7,1
a) \(2^{x-1}+2^{x+1}+2^{x+2}=104\)
=> \(2^{x-1}+2^x\cdot2+2^x\cdot2^2=104\)
=> \(2^x:2+2^x\cdot\left(2+2^2\right)=104\)
=> \(2^x\cdot\frac{1}{2}+2^x\cdot6=104\)
=> \(2^x\cdot\left(\frac{1}{2}+6\right)=104\Rightarrow2^x=104:\left(\frac{1}{2}+6\right)=104:\frac{13}{2}=16\)
=> \(x=4\)
a, \(21\in B\left(x-3\right)\Leftrightarrow x-3\inƯ\left(21\right)\Leftrightarrow x-3\in\left\{1;3;7;21;-1;-3;-7;-21\right\}\)
\(\Leftrightarrow x\in\left\{4;6;10;24;2;0;-4;-18\right\}\)
Vì \(x\in N\Rightarrow x\in\left\{4;6;10;24;2;0\right\}\)
b, \(1-x\inƯ\left(17\right)\Leftrightarrow1-x\in\left\{1;17;-1;-17\right\}\)
\(\Leftrightarrow x\in\left\{0;-16;2;18\right\}\)
Vì \(x\in N\Rightarrow x\in\left\{0;2;18\right\}\)
c, \(2x+3\in B\left(2x-1\right)\)
\(\Leftrightarrow2x+3⋮2x-1\Leftrightarrow2x-1+4⋮2x-1\Leftrightarrow4⋮2x-1\)
\(\Leftrightarrow2x-1\inƯ\left(4\right)\Leftrightarrow2x-1\in\left\{1;2;4;-1;-2;-4\right\}\)
\(\Leftrightarrow x\in\left\{1;\frac{3}{2};\frac{5}{2};0;\frac{-1}{2};\frac{-3}{2}\right\}\)
Vì \(x\in N\Rightarrow x\in\left\{1;0\right\}\)
d, \(x+1\inƯ\left(x^2+x+3\right)\Leftrightarrow x^2+x+3⋮x+1\Leftrightarrow x\left(x+1\right)+3⋮x+1\Leftrightarrow3⋮x+1\)
\(\Leftrightarrow x+1\inƯ\left(3\right)\Leftrightarrow x+1\in\left\{1;3;-1;-3\right\}\)
\(\Leftrightarrow x\in\left\{0;2;-2;-4\right\}\)
Vì \(x\in N\Rightarrow x\in\left\{0;2\right\}\)
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