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Bài 1.Tính
a) = ( -100 ); b) = ( -55 ); c) = ( -20 ); d) = 3125; e) ( -9 ); g) = ( -24 )
Bài 2. Tính
a) =190; b) = ( -310 ); c) = ( -330 ); d) =102 000; e) = ( -108 ); g) = ( -7 ).
Bài 3.Tính
a) = ( -250 ); b) ( -48 ); c) = ( -16 ); d) = 32; e) ( -3 ); g) = ( -9 ).
Bài 4. Giải
Chị An có: 500.5-600= 1900 đ
Chị Lan có: 500.3-1000= 500 đ
Chị Trang có: 500.6-400= 2600 đ
b) \(\left(5^{22}.7-5^{21}.10\right):25^{11}\)
\(=5^{21}.\left(5.7-10\right):5^{22}\)
\(=5^{21}.25:5^{22}=5^{21}.5^2:5^{22}=5^{23}:5^{22}=5\)
c) \(\dfrac{3^6.15^5+9^3.15^6}{3^{10}.5^2.2^3}=\dfrac{3^6.3^5.5^5+3^6.3^6.5^6}{3^{10}.5^2.2^3}\)
\(=\dfrac{3^{11}.5^5+3^{12}.5^6}{3^{10}.5^2.2^3}=\dfrac{3^{11}.5^5\left(1+3.5\right)}{3^{10}.5^2.2^3}\)
\(=\dfrac{3^1.5^3.16}{2^3}=\dfrac{3^1.5^3.2^4}{2^3}=3.125.2=750\)
d) \(\dfrac{11.27^7.3^8-9^{15}}{\left(2.3^{14}\right)^2}=\dfrac{11.3^{21}.3^8-3^{30}}{2^2.3^{28}}=\dfrac{11.3^{29}-3^{30}}{2^2.3^{28}}\)
\(=\dfrac{3^{29}\left(11-3\right)}{2^2.3^{28}}=\dfrac{3^1.8}{2^2}=\dfrac{3.2^3}{2^2}=3.2=6\)
Bài 1:
a: Ta có: \(\left|x+3\right|\ge0\forall x\)
\(\left|y-2\right|\ge0\forall y\)
Do đó: \(\left|x+3\right|+\left|y-2\right|\ge0\forall x,y\)
Dấu '=' xảy ra khi x=-3 và y=2
b: Ta có: \(\left|x+3\right|=4\)
\(\Leftrightarrow\left[{}\begin{matrix}x+3=4\\x+3=-4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-7\end{matrix}\right.\)
c: Ta có: \(\left|-x+5\right|=\left|1-5\right|\)
\(\Leftrightarrow\left|x-5\right|=4\)
\(\Leftrightarrow\left[{}\begin{matrix}x-5=4\\x-5=-4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=9\\x=1\end{matrix}\right.\)
Bài 16:
a: Ta có: \(\left|x\right|-x=0\)
\(\Leftrightarrow\left|x\right|=x\)
\(\Leftrightarrow x\ge0\)
b: Ta có: \(\left|x\right|+x=0\)
\(\Leftrightarrow\left|x\right|=-x\)
\(\Leftrightarrow x\le0\)
c: Ta có: \(\left|x\right|-5=-12+30\)
\(\Leftrightarrow\left|x\right|=18+5=23\)
hay \(x\in\left\{-23;-23\right\}\)
d: Ta có: \(-11-\left|x\right|=-17\)
\(\Leftrightarrow\left|x\right|=6\)
hay \(x\in\left\{6;-6\right\}\)
2: x+13 là bội của x-1
=>\(x+13⋮x-1\)
=>\(x-1+12⋮x-1\)
=>\(x-1\inƯ\left(12\right)\)
mà x-1>=-1(vì x là số tự nhiên)
nên \(x-1\in\left\{-1;1;2;3;4;6;12\right\}\)
=>\(x\in\left\{0;2;3;4;5;7;13\right\}\)
3: 4x+9 là bội của 2x+1
=>\(4x+9⋮2x+1\)
=>\(4x+2+7⋮2x+1\)
=>\(2x+1\in\left\{1;7\right\}\)
=>\(x\in\left\{0;3\right\}\)
Bài 16:
\(e,\left(6n+11\right)⋮\left(2n+3\right)\\ \Rightarrow\left[3\left(2n+3\right)+2\right]⋮\left(2n+3\right)\\ \Rightarrow2⋮\left(2n+3\right)\\ \Rightarrow2n+3\inƯ\left(2\right)=\left\{-2;-1;1;2\right\}\\ \Rightarrow n\in\varnothing\left(n\in N\right)\\ g,\left(3n+5\right)⋮\left(2n+1\right)\\ \Rightarrow\left(6n+10\right)⋮\left(2n+1\right)\\ \Rightarrow\left[3\left(2n+1\right)+7\right]⋮\left(2n+1\right)\\ \Rightarrow7⋮\left(2n+1\right)\\ \Rightarrow2n+1\inƯ\left(7\right)=\left\{-7;-1;1;7\right\}\\ \Rightarrow n\in\left\{0;3\right\}\left(n\in N\right)\)