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Gọi \(ƯCLN\left(6n+5;3n+2\right)\) là d.
\(\Rightarrow\hept{\begin{cases}6n+5⋮d\\3n+2⋮d\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}6n+5⋮d\\2\left(3n+2\right)⋮d\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}6n+5⋮d\\6n+4⋮d\end{cases}}\)
\(\Rightarrow\left(6n+5\right)-\left(6n+4\right)⋮d\)
\(\Rightarrow1⋮d\)
\(\Rightarrow d=1\)
\(\Rightarrow\left(6n+5;3n+2\right)=1\)
\(\Rightarrow\frac{6n+5}{3n+2}\) tối giản.
\(\frac{6n+5}{3n+2}\)tối giản
=>6n+5 chia hết cho 3n+2
=>(6n+5)-2(3n+2)chia hết cho 3n+2
=>6n+5-6n-4 chia hết cho 3n+2
=>1 chia hết cho 3n+2
=>đpcm
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\(\left(2x-1\right)\left(y^2-5\right)=12\)
\(\left(2x-1\right)\left(y^2-5\right)=12=1.12=12.1=2.6=6.2=3.4=4.3\)
\(\Rightarrow\orbr{\begin{cases}2x-1=1\\y^2-5=12\end{cases}\Rightarrow}\orbr{\begin{cases}2x=2\\y^2=17\end{cases}\Rightarrow\orbr{\begin{cases}x=1\\y=\sqrt{17}\end{cases}}}\)( loại )
\(\Rightarrow\orbr{\begin{cases}2x-1=12\\y^2-5=1\end{cases}\Rightarrow\orbr{\begin{cases}2x=13\\y^2=6\end{cases}\Rightarrow}}\orbr{\begin{cases}x=\frac{13}{2}\\y=\sqrt{6}\end{cases}}\)( loại )
Đến đây bạn tự làm típ nha :))))
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25 . 6 + 25 . 4 + 25 . 18 + 25 . 12
= 25 . (6 + 4 + 18 + 12)
= 25 . 40
= 1000
25 x 6 + 25 x 4 + 25 x 18 + 25 x 12
= 25 x ( 6 + 4 + 18 + 12 )
= 25 x 40
= 1 000
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a ) 420 + 65 . 4 = ( x + 175 ) : 51 + 30
420 + 260 = ( x + 175 ) : 51 + 30
680 = ( x + 175 ) : 51 + 30
=> ( x + 175 ) : 51 = 680 - 30
( x + 175 ) : 51 = 650
x + 175 = 650 . 51
x + 175 = 33150
x = 33150 - 175
x = 32975
b ) ( 32 . 15 ) : 2 = ( x + 70 ) : 14 - 40
480 : 2 = ( x + 70 ) : 14 - 40
240 = ( x + 70 ) : 14 - 40
=> ( x + 70 ) : 14 = 240 + 40
( x + 70 ) : 14 = 280
x + 70 = 280 . 14
x + 70 = 3920
x = 3920 - 70
x = 3850
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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: \(25\cdot57+75+33\cdot25+75\cdot89\)
\(=25\cdot57+25\cdot33+75+75\cdot89\)
\(=25\left(57+33\right)+75\left(1+89\right)\)
\(=25\cdot100+100\cdot75\)
\(=100\left(25+75\right)=100\cdot100=10000\)