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9/2-1/2-1+3x=1/2+1/3
=)8/2-1+3x=5/6
=)3+3x=5/6
=)3x=5/6-3
=)3x=13/6
x=13/18
ta có: 9/2 - 1/2 - (1-3x)=1/2 + 1/3
<=>9/2 - 1/2 - (1-3x)=5/6
<=>1/2 - (1-3x) =9/2-5/6
<=>1/2 - (1-3x) =11/3
<=> 1 - 3x = 19/6
<=> 3x =13/6
<=> x =13/18
\(3^{x+2}+3^x=10\)
\(3^x\cdot\left(3^2+1\right)=10\)
\(3^x\cdot\left(9+1\right)=10\)
\(3^x\cdot10=10\)
\(3^x=10:10\)
\(3^x=1\)
\(3^x=3^0\)
\(\Rightarrow x=0\)
3n + 4 = 3n - 6 + 10
= 3(n - 2) + 10
Để (3n + 4) ⋮ (n - 2) thì 10 ⋮ (n - 2)
⇒ n - 2 ∈ Ư(10) = {-10; -5; -2; -1; 1; 2; 5; 10}
⇒ n ∈ {-8; -3; 0; 1; 3; 4; 7; 12}
Mà n là số tự nhiên
⇒ n ∈ {0; 1; 3; 4; 7; 12}
\(3,8276< \overline{3,8ab5}< 3,836\)
=>\(276< \overline{ab5}< 360\)
=>\(\left(a,b\right)\in\left\{\left(2;8\right);\left(2;9\right);\left(3;0\right);\left(3;1\right);\left(3;2\right);\left(3;3\right);\left(3;4\right);\left(3;5\right)\right\}\)
\(A=2+2^2+2^3+...+2^{260}\)
\(A=2\left(1+2\right)+2^2\left(1+2\right)+2^3\left(1+2\right)+...+2^{259}\left(1+2\right)\)
\(A=2.3+2^2.3+2^3.3+...+2^{259}.3\)
\(A=3\left(2+2^2+2^3+...+2^{259}\right)⋮3\left(1\right)\)
\(A=\left(2+2^2+2^3\right)+...+\left(2^{258}+2^{259}+2^{260}\right)\)
\(A=2.\left(1+2+2^2\right)+...+2^{258}.\left(1+2+2^2\right)\)
\(A=2.7+...+2^{258}.7\Rightarrow A=7\left(2+...+2^{258}\right)⋮7\left(2\right)\)
\(A=\left(2+2^2+2^3+2^4\right)+...+\left(2^{257}+2^{258}+2^{259}+2^{260}\right)\)
\(A=2.\left(1+2+2^2+2^3\right)+...+2^{257}.\left(1+2+2^2+2^3\right)\)
\(A=2.15+...+2^{257}.15\Rightarrow A=15\left(2+...+2^{257}\right)⋮5\left(15⋮5\right)\left(3\right)\)
\(\left(1\right),\left(2\right),\left(3\right)\Rightarrow dpcm\)