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Cậu 14: x - {[- x +(x+ 3)]} - [( x + 3) - (x-2)] = 0
Giúp mình với ạ, mình cần gấp
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x + 6 chia hết cho x + 3
=> x + 3 + 3 chia hết cho x + 3
=> 3 chia hết cho x + 3
=> (x + 3) \(\in\) Ư(3)
=> (x + 3) \(\in\) {-3; -1; 1; 3}
=> x \(\in\) {-6; -4; -2; 0}
![](https://rs.olm.vn/images/avt/0.png?1311)
Gọi d=ƯC(2n+7;5n+17)
\(\Rightarrow\left\{{}\begin{matrix}2n+7⋮d\\5n+17⋮d\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}10n+35⋮d\\10n+34⋮d\end{matrix}\right.\)
\(\Rightarrow1⋮d\Rightarrow d=1\)
\(\Rightarrow\) phân số \(\dfrac{2n+7}{5n+17}\) tối giản
\(2A=\dfrac{4}{1.5}+\dfrac{6}{5.11}+\dfrac{8}{11.19}+\dfrac{10}{19.29}+\dfrac{12}{29.41}\)
\(2A=1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{19}+\dfrac{1}{19}-\dfrac{1}{29}+\dfrac{1}{29}-\dfrac{1}{41}\)
\(2A=1-\dfrac{1}{41}=\dfrac{40}{41}\)
\(A=\dfrac{40}{41}:2=\dfrac{20}{41}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
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Ta có : \(12a+7b=64\)
Do \(64⋮4,12a⋮4\) \(\Rightarrow7b⋮4\) mà \(\left(7,4\right)=1\)
\(\Rightarrow b⋮4\) (1)
Từ giả thiết \(\Rightarrow7b\le64\) \(\Leftrightarrow b\le9\) kết hợp với (1)
\(\Rightarrow b\in\left\{4,8\right\}\)
+) Với \(b=4\) thì : \(12a+7\cdot4=64\)
\(\Leftrightarrow12a=36\)
\(\Leftrightarrow a=3\) ( thỏa mãn )
+) Với \(b=8\) thì \(12a+7\cdot8=64\)
\(\Leftrightarrow12a=8\)
\(\Leftrightarrow a=\frac{8}{12}\) ( loại )
Vậy : \(\left(a,b\right)=\left(3,4\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
11: \(27+12+\left(-17\right)+\left(-12\right)\)
\(=\left(27-17\right)+\left(12-12\right)\)
=10+0
=10
12: \(-564-\left(324-564-224\right)\)
\(=-564-\left(-564+100\right)\)
\(=-564+564-100=-100\)
13: \(2^3\cdot3^2-7^2-2022^0\)
\(=8\cdot9-49-1\)
=72-50
=22
14: \(236\cdot145+236\cdot856-236\)
\(=236\cdot145+236\cdot856-236\cdot1\)
\(=236\left(145+856-1\right)\)
\(=236\cdot1000=236000\)
15: \(-\left(-357\right)+27+\left(-357\right)+\left(-32\right)\)
\(=357+27-357-32\)
=27-32
=-5
16: \(275\cdot48+22\cdot275+175\left(-70\right)\)
\(=275\left(48+22\right)-175\cdot70\)
\(=275\cdot70-175\cdot70\)
\(=70\left(275-175\right)=70\cdot100=7000\)
17: \(\dfrac{\left(23\cdot36-17\cdot36\right)}{36}\)
\(=\dfrac{36\left(23-17\right)}{36}\)
=23-17
=6
18: \(3\cdot5^3-27:3^2+5^3\cdot4-18:3^2\)
\(=3\cdot5^3+4\cdot5^3-27:9-18:9\)
\(=5^3\left(3+4\right)-3-2\)
\(=125\cdot7-5=875-5=870\)
19: \(-87+\left(-12\right)-\left(-487\right)+512\)
\(=-87-12+487+512\)
\(=\left(487-87\right)+\left(512-12\right)\)
=400+500
=900
20: \(25\cdot57+75+33\cdot25+75\cdot89\)
\(=25\cdot57+25\cdot33+75+75\cdot89\)
\(=25\left(57+33\right)+75\left(1+89\right)\)
\(=25\cdot100+100\cdot75\)
\(=100\left(25+75\right)=100\cdot100=10000\)
![](https://rs.olm.vn/images/avt/0.png?1311)
B = 1+1³+1⁴+...+1⁹⁸+1⁹⁹
B1 = 1³+1⁵+...+1⁹⁹+1¹⁰⁰
B1-B =(1³+1⁵+...+1⁹⁹+1¹⁰⁰) - ( 1+1³+1⁴+...+1⁹⁸+1⁹⁹ )
B0 = 1¹⁰⁰ - 1⁹⁹
B = 1