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1, ( x - 3 )100 - 1 = 0 => ( x - 3 )100 = 0 + 1 = 1
Mà 1 = 1100 => x - 3 = 1 => x = 1 + 3 = 4 hoặc 1 = (-1)100 => x - 3 = -1 => x = -1 + 3 = 2
2, ( 9 - 5x )2019 + 1 = 0 => ( 9 - 5x )2019 = 0 - 1 = -1
Mà -1 = (-1)2019 => 9 - 5x = -1 => 5x = 9 - ( -1 ) = 10 => x = 10 : 5 = 2
3, ( 4x - 3 )5 = ( 2 - x )5 => 4x - 3 = 2 - x
=> 4x + x = 3 + 2 => 5x = 5 => x = 5 : 5 = 1
4, ( 2x - 9 )2 = ( 5x - 6 )2 => 2x - 9 = 5x - 6 ... ( tự làm )
5, ( 11 - 4x )6 - ( 2 - 5x )6 = 0 => ( 11- 4x )6 = ( 2 - 5x )6
=> 11 - 4x = 2 - 5x _ Đến đây làm tương tự 2 câu trên
6, ( x - 9 )9 = ( x - 9 )7 mà cơ số bằng nhau ( = x - 9 )
=> x - 9 = 1 hoặc -1 vì 19 = 17 và ( -1 )9 = ( -1 )7
TH1: x - 9 = 1 => x = 1 + 9 = 10
TH2: x - 9 = -1 => x = -1 + 9 = 8
7, 8, 9 tương tự 6 ( kết quả của cơ số đều = 1 hoặc -1 )
a) \(44:22+58.6-2\)
\(=2+348-2\)
\(=348\)
b) \(6^2:4,3+2.5^2-2018^0\)
= \(36:4,3+2.25-1\)
\(\approx8,4+50-1\)
\(\approx57,4\)
c) \(\left|-12\right|+\left[-14+2^5:3^3\right]\)
= \(12+\left[-14+32:27\right]\)
\(\approx12+\left[-14+1,2\right]\)
\(\approx12-13,2\)
\(\approx-1,2\)
\(A=3^0+3^1+3^2+......+3^{2018}\)
\(3A=3.\left(3^0+3^1+3^2+.....+3^{2018}\right)\)
\(3A=3^1+3^2+3^3+........+3^{2019}\)
\(3A-A=\left(3^1+3^2+3^3+......+3^{2019}\right)-\left(3^0+3^1+3^2+.....+3^{2018}\right)\)
\(2A=3^{2019}-3^0\)
\(A=\left(3^{2019}-3^0\right):2\)
\(B=6^{10}+6^{11}+6^{12}+....+6^{2012}\)
\(6B=6.\left(6^{10}+6^{11}+6^{12}+.....+6^{2012}\right)\)
\(6B=6^{11}+6^{12}+6^{13}+.......+6^{2013}\)
\(6B-B=\left(6^{11}+6^{12}+6^{13}+......+6^{2013}\right)-\left(6^{10}+6^{11}+6^{12}+.......+6^{2012}\right)\)
\(5B=6^{2013}-6^{10}\)
\(B=\left(6^{2013}-6^{10}\right):5\)
A=(1-2)+(3-4)+...+(999-1000)
có 1000 số hạng
A=(-1)+(*1)+...+(-1)
có 500 số hạng
A=-1*500
A=-500
\(\dfrac{5.4^2+16}{2^3}=\dfrac{16\left(5+1\right)}{2^3}=2.6=12\)
\(\dfrac{5^{16}}{5^{14}}+2^2.2^3=5^2+2^5=25+32=57\)
\(\dfrac{7^{2012}}{7^{2010}}-6^2=7^2-6^2=49-36=13\)
\(2^2.3+\dfrac{250}{5^2}=12+10=22\)
\(2.9.50-2012^0=9.100-1=899\)
\(\dfrac{123}{3}-\dfrac{4^3}{2^4}=41-\dfrac{4^2.4}{2^4}41-4=37\)
\(A=2^2+2^4+2^6+.....+2^{2012}\)
\(\Rightarrow2^2A=2^4+2^6+2^8+.....+2^{2014}\)
\(\Rightarrow4A-A=\left(2^4+2^6+....+2^{2014}\right)-\left(2^2+2^4+....+2^{2012}\right)\)
\(\Rightarrow3A=2^{2014}-2^2\)
\(\Rightarrow A=\frac{2^{2014}-2^2}{3}\)
Ta có: A= 22 + 24 + 26 + 28 +...... 22012
=> 22A = 24 + 26 + 28 +...... 22014
=> 4A - A = 22014 - 22
=> 3A =
B= 3 - 32 + 33 - 34 + 35 - 36 + ..... - 32012
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
e, \(E=\dfrac{4^6.3^4.9^5}{6^{12}}=\dfrac{\left(2^2\right)^6.3^4.\left(3^2\right)^5}{2^{12}.3^{12}}\)
\(=\dfrac{3^4.3^{10}}{3^{12}}=3^2=9\)
f, \(F=\dfrac{2^{13}+2^5}{2^{10}+2^2}=\dfrac{2^5.\left(2^8+1\right)}{2^2.\left(2^8+1\right)}=2^3=8\)
g, \(G=\dfrac{21^2.141.125}{35^{5.6}}=\dfrac{3^2.7^2.47.3.5^3}{5^{30}.7^{30}}\)
\(=\dfrac{3^3.47}{5^{27}.7^{28}}\)(bạn xem lại đề nha)
Các câu còn lại làm tương tự! Chúc bạn học tốt!!!
\(A=\left(6^{2019}-6^{2018}\right):6^{2018}\)
\(=6^{2019}:6^{2018}-6^{2018}:6^{2018}\)
\(=6-1\)
\(=5\)
\(B=234:\left\{3.\left[47-\left(4^2+5\right)\right]\right\}\)
\(=234:\left[3.\left(47-21\right)\right]\)
\(=234:\left(3.26\right)\)
\(=234:78\)
\(=3\)
\(D=2.\left[\left(7-3^3:3^2\right):2^2+99\right]-100\)
\(=2.\left[\left(7-3\right):4+99\right]-100\)
\(=2.\left(1+99\right)-100\)
\(=100.\left(2-1\right)\)
\(=100\)
\(5^2\cdot6:\left[2016^0\cdot\left(128-5^3\right)\right]\)
\(=25\cdot6:\left[1\cdot\left(128-125\right)\right]\)
\(=25\cdot6:\left[1\cdot3\right]\)
\(=25\cdot6:3\)
\(=150:3\)
\(=50\)
\(\left(2^{2018}:2^{2012}-6^2\right)-\left[\left(35-22\right)^2-6^2\right]\)
\(=\left(2^6-6^2\right)-\left[13^2-6^2\right]\)
\(=\left(64-36\right)-\left[169-36\right]\)
\(=28-133\)
\(=-105\)