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CÂU 1
\(5^{n+1}+5^n=750\)
\(=>5^n\cdot5+5^n=750\)
\(=>5^n\cdot\left(5+1\right)=750\)
\(=>5^n\cdot6=750\)
\(=>5^n=750:6\)
\(=>5^n=125\)
\(=>5^n=5^3\)
\(=>n=3\)
1) x - 36 + 12 = - x+ 10
=> x + x = 10 + 24
=> 2x = 34
=> x = 34/2 = 17
2) (x + 15) - (11 - x) = (-2)2
=> x + 15 - 11 + x = 4
=> 2x = 4 - 4
=> 2x = 0
=> x = 0
3) 40 - 4x2 = (-6)2
=> 40 - 4x2 = 36
=> 4x2 = 40 - 36
=> 4x2 = 4
=> x2 = 1
=> x = \(\pm\)1
4) (-50) + 10x2 = (-25) x |-2|
=> -50 + 10x2 = -50
=> 10x2 = -50 + 50
=> 10x2 = 0
=> x2 = 0
=> x = 0
5) |x + 1| = 2020
=> \(\orbr{\begin{cases}x+1=2020\\x+1=-2020\end{cases}}\)
=> \(\orbr{\begin{cases}x=2019\\x=-2021\end{cases}}\)
6) (x + 1)5 + 8 = 0 (xem lại đề)
7) (-20) + x3 : 16 = -24
=> x3 : 16 = -24 + 20
=> x3 : 16 = -4
=> x3 = -4 . 16
=> x3 = -64 = (-4)3
=> x = -4
9) x14 = x17
=> x14 - x17 = 0
=> x14(1 - x3) = 0
=> \(\orbr{\begin{cases}x^{14}=0\\1-x^3=0\end{cases}}\)
=> \(\orbr{\begin{cases}x=0\\x=1\end{cases}}\)
10) (-36) + (1 - x)2 = 0
=> (1 - x)2 = 36
=> (1 - x)2 = 62
=> \(\orbr{\begin{cases}1-x=6\\1-x=-6\end{cases}}\)
=> \(\orbr{\begin{cases}x=-5\\x=7\end{cases}}\)
số sh cua tong A bang so hang cua day so cach deu 1 don vi tu 1 den 60
so sh cua tong A la:(60-1):1+1=60 (sh)
Cu 3 sh lien tiep cua tong A nhom thanh 1 nhom thi ta duoc so nhom la : 60: 3=20(nhom)
khi do : A = (2+2^2+2^3)+(2^4+2^5+2^6)+(2^7+2^8+2^9)+....+(2^58+2^59+2^60)
A=(2+2.2+2.2^2)+(2^4+2^4.2+2^4.2^2)+(2^7+2^7.2+2^7.2^2)+.....+(2^58
2^58.2+2^58.2^2)
A=2(1+2+2^2)+2^4(1+2+2^2)+2^7(1+2+2^2)+...+2^58(1+2+2^2)
A=2.7+2^4.7+2^7.7+...+2^58.7
A=7(2+2^4+2^7+...+2^58)
Vi 7 chia het cho 7
2+2^4+2^7+...+2^58 thuoc N
Suy ra 7(2+2^4+2^7+...+2^58) chia het cho 7
hay A chia het cho 7
Vay A chia het cho 7
Câu 1:
abc >/ 100 ; bca >/ 100 ; cab>/100
< = > abc + bca + cab >/300
< = > abc + bca + cab >/ 111
\(a)47-\left[\left(45.2^4-5^2.12\right):14\right]\)
\(=47-\left[\left(45.16-25.12\right):14\right]\)
\(=47-\left[\left(720-300\right):14\right]\)
\(=47-\left[420:14\right]\)
\(=47-30\)
\(=17\)
\(b)50-\left[\left(20-2^3\right):2+34\right]\)
\(=50-\left[\left(20-8\right)\right]:2+34\)
\(=50-\left[12:2+34\right]\)
\(=50-\left[6+34\right]\)
\(=50-40\)
\(=10\)
\(c)10^2-\left[60:\left(5^6:5^4-3,5\right)\right]\)
\(=10^2-\left[60:\left(5^2-3,5\right)\right]\)
\(=10^2-\left[60:\left(25-3,5\right)\right]\)
\(=10^2-\left[60:21,5\right]\)
\(=100-\dfrac{120}{43}\)
\(=\dfrac{4180}{43}\)
\(d)50-\left[\left(50-2^3.5\right):2+3\right]\)
\(=50-\left[\left(50-8.5\right):2+3\right]\)
\(=50-\left[\left(50-40\right):2+3\right]\)
\(=50-\left[10:2+3\right]\)
\(=50-5+3\)
\(=50-8\)
\(=42\)
\(e)10-\left[\left(8^2-48\right).5+\left(2^3.10+8\right)\right]:28\)
\(=10-\left[\left(64-48\right).5+\left(8.10+8\right)\right]:28\)
\(=10-\left[16.5+\left(80+8\right)\right]:28\)
\(=10-\left[80+88\right]:28\)
\(=10-168:28\)
\(=10-6\)
\(=4\)
\(f)8697-\left[3^7:3^5+2.\left(13-3\right)\right]\)
\(=8697-\left[3^2+2.\left(13-3\right)\right]\)
\(=8697-\left[9+2.10\right]\)
\(=8697-9+20\)
\(=8697-29\)
\(=8668\)
\(g)2011+5\left[300-\left(17-7\right)^2\right]\)
\(=2011+5.\left[300-10^2\right]\)
\(=2011+5.\left[300-100\right]\)
\(=2011+5.200\)
\(=2011+1000\)
\(=3011\)
\(h)695-\left[200+\left(11-1\right)^2\right]\)
\(=695-\left[200+10^2\right]\)
\(=695-200+100\)
\(=695-300\)
\(=395\)
\(i)129-5\left[29-\left(6-1\right)^2\right]\)
\(=129-5\left[29-5^2\right]\)
\(=129-5\left[29-25\right]\)
\(=129-5.4\)
\(=129-20\)
\(=109\)
a, \(A=2015.20162016-2016.20152015\)
\(A=2015.\left(2016.10001\right)-2016.20152015\)
\(A=\left(2015.10001\right).2016-20152015.2016\)
\(A=20152015.2016-20152015.2016\)
\(A=0\)
Vậy A = 0
b, \(B=\left(3.4.2^{16}\right)^2\div11.2^{13}.4^{11}-16^9\)
\(B=3^2.2^4.2^{32}\div11.2^{13}.\left(2^2\right)^{11}-\left(2^4\right)^9\)
\(B=3^2.2^4.2^{32}\div11.2^{13}.2^{22}-2^{36}\)
\(B=3^2.2^{36}\div11.2^{35}-2^{36}\)
\(B=3^2.2^{35}.2\div11.2^{35}-2.2^{35}\)
\(B=3^2.2\div9=9.2\div9=2\)
Vậy B = 2
c, \(C=2^{10}.13+2^{10}.65\div2^8.104\)
\(C=2^{10}.\left(13+65\right)\div2^8.104\)
\(C=2^{10}.78\div2^8.104\)
\(C=2^{10}.39\div2^8.13\)
\(C=39\div13=3\)
Vậy C = 3
Đề bài câu c sai mk sửa nhé là 28 ms tính đc k nó dư lắm !!!
b) 1449 - {[(216 + 184) : 8] . 9}
= 1449 - {[400 : 8] : 9}
= 1449 - {50 : 9}
= 1449 - \(\frac{50}{9}\)
= \(\frac{12991}{9}\)
c) 342 . 163 + 337 . 342 - 103 . 171
= 342 . (163 + 337) - 1000 . 171
= 342 . 500 - 500 . 2 . 171
= 500 . (342 - 2 - 171)
= 500 . 169
= 84500
Câu 1:
a. 19.64 + 36.19
=19.(64+36)
=19.100
=1900
b.22.3 - ( 110+ 8 ) : 32
=4.3-(1+8) : 9
=12 - 9:9
=12-1
=11
c. 150 - [ 102 - (14 - 11)2 .20070
=150-[100-32.1]
=150-[100-9]
=150-91
=59
A = 23 . 19 - 23 . 14 + 12018
= 23.(19 - 14) + 1
= 8 . 5 + 1
= 40 + 1 = 41
B = 102 - [60 : (56 : 54 - 3. 5)]
= 100 - [60 : (10 - 15)]
= 100 - [60 : (-5)]
= 100 + 12
= 112
a) Ta có:
10^n + 8
= 1000..0 + 8 ( n số 0)
= 100...08 ( n - 1 số 0 )
Tổng các chữ số là: 1 + 0 + .. + 0 + 8 = 9 chia hết cho 9
=>100..00 8 chia hết cho 9
=> 10^n +8 chia hết cho 9
b) \(1531\) và \(2001\) là số lẻ nên tổng của chúng là số chẵn hay tổng của chúng chia hết cho \(2\).
c) Ta có: 10n+53=10.........0+125=100.....0125
\(\Rightarrow\) tổng các chữ số là: 1+0+...+0+1+2+5=9
Vì tổng các chữ số của 10n+53 \(⋮\) 3 và 9 ( \(9⋮\)3 và 9) nên 10n+53 chia hết cho 3 và 9.
a) Ta có: \(19\cdot64+36\cdot19\)
\(=19\cdot\left(64+36\right)\)
\(=19\cdot100=1900\)
b) Ta có: \(150-\left[10^2-\left(14-11\right)^2\cdot2700^0\right]\)
\(=150-\left[100-3^2\cdot1\right]\)
\(=150-91\)
\(=69\)
c) Ta có: \(22^3-\left(1^{10}+8\right):3^2\)
\(=22^3-\left(1+8\right):3^2\)
\(=22^3-9:9\)
\(=22^3-1\)
\(=10647\)
d) Ta có: \(59-\left[90-\left(17-8\right)^2\right]\cdot1^{4514}\)
\(=59-\left[90-9^2\right]\cdot1\)
\(=59-\left(90-81\right)\)
\(=59-9=50\)
e) Ta có: \(7^2-36:3^2\)
\(=7^2-36:9\)
\(=49-4=45\)