Tổng vận tốc của hai xe là 54:3=18(km/h)

Vận tốc của An là (18+6):2=12(km/h)

Vận tốc của Bình là 12-6=6(km/h)

Đúng hay sai nhỉ mn

`a) 7 . (x - 4) : 3 = 7`

`=> 7 (x - 4) = 7.3`

`=> 7(x - 4) = 21`

`=> x - 4 = 21 : 7`

`=> x - 4 = 3`

`=> x = 3+4`

`=> x = 7`

Vậy `x = 7`

`b) 12x -40 : 4=2`

`=> 12x - 10 = 2`

`=> 12x = 2+10`

`=> 12x = 12`

`=> x = 12 : 12`

`=> x = 1`

Vậy `x = 1`

`c) 8+3-x = 23`

`=> 11 - x = 23`

`=> x = 11 - 23`

`=> x = -12`

Vậy `x = -12`

Cảm ơn bạn nhá hoàng anh

`BCN``N(a,b) = 15`

`=> 15 ⋮ a` và `15 ⋮ b`

`=> a;b ∈` {`-15;-5;-3;-1;1;3;5;15`}

Mà `a+b = 20`

`=> a;b ∈` {`5;15`} 

Vậy `(a;b) ∈` {`(5;15),(15;5)`}

Bài 2:

\(a,2^{10}+2^9\\ =2^9\cdot\left(2+1\right)\\ =3\cdot2^9⋮3\\ b,2^{10}+2^9+2^8\\ =2^8\cdot\left(2^2+2+1\right)\\ =7\cdot2^8⋮7\\ c,5^{2023}+5^{2022}\\ =5^{2022}\cdot\left(5+1\right)\\ =6\cdot5^{2022}⋮6\\ d,2^{10}-3\cdot2^7\\ =2^7\cdot\left(2^3-3\right)\\ =5\cdot2^7⋮5\\ e,7^{10}-7^8\\ =7^8\cdot\left(7^2-1\right)\\ =7^8\cdot48⋮48\\ f,16^5+2^{15}\\ =\left(2^4\right)^5+2^{15}\\ =2^{20}+2^{15}\\ =2^{15}\cdot\left(2^5+1\right)\\ =33\cdot2^{15}⋮33\\ g,8^8+4^{10}\\ =\left(2^3\right)^8+\left(2^2\right)^{10}\\ =2^{24}+2^{20}\\ =2^{20}\cdot\left(2^4+1\right)\\ =17\cdot2^{20}⋮17\\ h,81^7-27^9-9^{13}\\ =\left(3^4\right)^7-\left(3^3\right)^9-\left(3^2\right)^{13}\\ =3^{28}-3^{27}-3^{26}\\ =3^{26}\cdot\left(3^2-3-1\right)\\ =3^{26}\cdot5\\ =3^{24}\cdot\left(3^2\cdot5\right)\\ =45\cdot3^{24}⋮45\)

`(x-5)^2024=(2024^2025*2025^2024)^0`

`=>(x-5)^2024=1`

`=>(x-5)^2024=1^2024`

`TH1:x-5=1`

`=>x=5+1`

`=>x=6`

`TH2:x-5=-1`

`=>x=-1+5`

`=>x=4` 

Bài 2:

\(1)25-12\cdot2+2^3\\ =25-24+2^3\\ =1+8\\ =9\\ 2)45-12\cdot3+2^3\\ =45-36+2^3\\ =9+8\\ =17\\ 3)32+5\cdot13-3\cdot2^3\\ =32+65-3\cdot8\\ =97-24\\ =73\\ 4)150+50:5-2\cdot3^2\\ =150+10-2\cdot9\\ =160-18\\ =142\\ 5)35-2\cdot1^{111}+3\cdot7^2\\ =35-2\cdot1+3\cdot49\\ =35-2+147\\ =33+147\\ =180\\ 6)2023-5^3:25+27\\ =2023-125:25+27\\ =2023-5+27\\ =2023+22\\ =2045\)

Bài 1:

1: \(3^2\cdot5^3+9^2=9\cdot125+81=1206\)

2: \(55+45:3^2=55+45:9=55+5=60\)

3: \(8^3:4^2-5^2=\dfrac{2^6}{2^4}-25=2^2-25=4-25=-21\)

4: \(5\cdot3^2-32:2^2=5\cdot9-2^3=45-8=37\)

5: \(16:2^3+5^2\cdot4=16:8+25\cdot4=2+100=102\)

6: \(5\cdot2^2-18:3^2=5\cdot4-18:9=20-2=18\)

7: \(3\cdot5^2-15\cdot2^2=3\cdot25-15\cdot4=75-60=15\)

8: \(2^3\cdot6-72:3^2=8\cdot6-72:9=48-8=40\)

9: \(5\cdot2^2-27:3^2=5\cdot4-27:9=20-3=17\)

10: \(3\cdot2^4+81:3^2=3\cdot16+81:9=48+9=57\)

11: \(4\cdot5^3-32:2^5=4\cdot125-32:32=500-1=499\)

12: \(6\cdot5^2-32:2^4\)

\(=6\cdot25-32:16\)

=150-2=148

Bài 3:

1: \(2^8:2^4+3^2\cdot3\)

\(=2^4+3^3\)

=16+27=43

2: \(3^{24}:3^{21}+2^2\cdot2^3\)

\(=3^3+2^5\)

=27+32=59

3: \(5^9:5^7+12\cdot3+7^0\)

\(=5^2+4+1\)

=25+5=30

4: \(5^6:5^4+3^2-2021^0\)

\(=5^2+9-1\)

=25+8=33

5: \(3^{19}:3^{16}+5^2\cdot2^3-1^{2021}\)

\(=3^3+25\cdot8-1\)

=200+26=226

6: \(3^6:3^5+2\cdot2^3+2021^0\)

\(=3+2^4+1\)

=4+16=20

\(\left[19\left(4\cdot2^3+18\right)-9\cdot50\right]:5^2\\ =\left[19\left(4\cdot8+18\right)-450\right]:25\\ =\left[19\cdot50-450\right]:25\\ =\left[950-450\right]:25\\ =500:25\\ =20\)

\(\left[19\left(4\cdot2^3+18\right)-9\cdot50\right]:5^2\\ =\left[19\left(4\cdot8+18\right)-9\cdot50\right]:25\\ =\left[19\left(32+18\right)-9\cdot50\right]:25\\ =\left(19\cdot50-9\cdot50\right):25\\ =50\cdot\left(19-9\right):25\\ =\left(50:25\right)\cdot10\\ =2\cdot10\\ =20\)

\(n\left(n+1\right)\left(2n+1\right)\\ =n\left(n+1\right)\left[2n-2+3\right]\\ =n\left(n+1\right)\left(2n-2\right)+3n\left(n+1\right)\\ =2\left(n-1\right)n\left(n+1\right)+3n\left(n+1\right)\)

Ta có:

`+)(n-1)n(n+1)` là tích của 3 số tự nhiên liên tiếp `=>(n-1)n(n+1)` chia hết cho 3 

`=>2(n-1)n(n+1)` chia hết cho 6 (1) 

`+)n(n+1)` là tích của 2 số tự nhiên liên tiếp `=>n(n+1)` chia hết cho 2

`=>3n(n+1)` chia hết cho 6 (2)

Từ (1) và (2) => `n(n+1)(2n+1)` chia hết cho 6