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Bài 1:
a: =>13x+8=9x+20
=>4x=12
hay x=3
b: \(\Leftrightarrow5x-7=-8-11-3x\)
=>5x-7=-3x-19
=>8x=-12
hay x=-3/2
c: \(\Leftrightarrow\left[{}\begin{matrix}12x-7=5\\12x-7=-5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=\dfrac{1}{6}\end{matrix}\right.\)
e: =>3x+1=-5
=>3x=-6
hay x=-2
a)
(=)8x=64
(=)x=8
b)
(=) |x+3|=7
+) x+3=7
(=) x=4
+) x+3=-7
(=) x=-10
c)
(=) (x-7)2 = 9 = 32 =(-3)2
+) x-7=3
(=)x=10
+)x-7=-3
(=)x=4
#Note: sau mỗi câunhớ kết luận vs " Vậy x=... thì ( ghi lại đề)"
#Học-tốt
Thiếu đk của x bạn ơi, mình xét x thuộc N* vậy
a) \(27^5>81^x\)
\(3^{15}>3^{4x}\)
=> 15 > 4x
=> a = { 1; 2; 3 }
b) \(125^{2+x}>25^8\)
\(5^{3x+6}>5^{16}\)
=> 3x + 6 > 16
=> 3x > 10
=> x > 4
c) \(x^{2018}=x^{18}\)
\(x^{2018}-x^{18}=0\)
\(x^{18}\left(x^{2000}-1\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x^{18}=0\\x^{2000}=1\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=0\\x=\left\{1;-1\right\}\end{cases}}\)
Vậy x = { -1; 0; 1 }
a, \(27^5>81^x\)
\(\Rightarrow3^{15}>3^{4x}\)
\(\Rightarrow15>4x\)
\(\Rightarrow3,75>x\)
\(\Rightarrow x=0;1;2;3\)
b, \(125^{2+x}>25^8\)
\(\Rightarrow5^{3\left(2+x\right)}>5^{16}\)
\(\Rightarrow5^{6+3x}>5^{16}\)
\(\Rightarrow6+3x>16\)
\(\Rightarrow3x>10\)
\(\Rightarrow x>3,\left(3\right)\)
\(\Rightarrow x=4;5;6;...\)
c, \(x^{2018}=x^{18}\)
\(\Rightarrow x^{2018}-x^{18}=0\)
\(\Rightarrow x^{18}\left(x^{2000}-1\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x^{18}=0\\x^{2000}-1=0\end{cases}\Rightarrow\orbr{\begin{cases}x=0\\x^{2000}=1\end{cases}\Rightarrow}\orbr{\begin{cases}x=0\\x=\pm1\end{cases}}}\)
\(x^{2018}-x^{18}=0\)
\(x^{18}.\left(x^{2018}-1\right)=0\)
\(=>\orbr{\begin{cases}x^{18}=0\\x^{2018}-1=0\end{cases}}\)
\(=>\orbr{\begin{cases}x=0\\x=1\end{cases}}\)
b) 275 > 81x
<=> 315 > 34x
<=> 15 > 4x
<=> x < 15 /4
c) 1252+x > 258
<=> 53(2+x) > 516
<=> 3(2+x) > 16
<=> 6 + 3x > 16
<=> 3x > 10
<=> x > 10/3
d) 5x . 5x+1 . 5x+2 <= 100...0 ( 18 số 0 ) : 218
<=> 5x+x+1+x+2 <= 1018 : 218
<=> 53x+3 <= 518
<=> 3x+3 <= 18
<=> 3x <= 15
<=> x <= 5
( <= là bé hơn hoặc bằng )
a) Ta có: \(\frac{9}{25}=\left(\frac{3}{5}\right)^2=\left(\frac{-3}{5}\right)^2\)
TH1: \(\Rightarrow\left(2x+\frac{3}{5}\right)^2=\left(\frac{3}{5}\right)^2\)
\(\Rightarrow2x+\frac{3}{5}=\frac{3}{5}\)
\(\Rightarrow2x=0\)
\(\Rightarrow x=0\)
TH2: \(2x+\frac{3}{5}=\frac{-3}{5}\Rightarrow2x=\frac{-6}{5}\Rightarrow x=\frac{-3}{5}\)
b) \(3\left(3x-\frac{1}{2}\right)^3+\frac{1}{9}=0\)
\(\Rightarrow3\left(3x-\frac{1}{2}\right)^3=\frac{-1}{9}\)
\(\Rightarrow\left(3x-\frac{1}{2}\right)^3=\frac{-1}{27}\)
Mà \(\frac{-1}{27}=\left(-\frac{1}{3}\right)^3\)
\(\Rightarrow3x-\frac{1}{2}=\frac{-1}{3}\Leftrightarrow3x=\frac{1}{6}\Rightarrow x=\frac{1}{18}\)
c) \(-5\left(x+\frac{1}{5}\right)-\frac{1}{2}\left(x-\frac{2}{3}\right)=\frac{2}{3}x-\frac{5}{6}\)
\(\Rightarrow-5x-1-\frac{1}{2}x+\frac{1}{3}-\frac{2}{3}x+\frac{5}{6}=0\)
\(\Rightarrow-\frac{37}{6}x=\frac{-1}{6}\Rightarrow x=\frac{1}{37}\)
d) \(3\left(x-\frac{1}{2}\right)-5\left(x+\frac{3}{5}\right)=x+\frac{1}{5}\)
\(\Rightarrow3x-\frac{3}{2}-5x-3-x-\frac{1}{5}=0\)
\(\Rightarrow-3x=\frac{47}{10}\Rightarrow x=\frac{-47}{30}\)
làm bài & thôi :
(x2 - 2x + 3) \(⋮\)(x - 1)
= x2 - 2x + 3
=) x2 - 2x + 3 - ( x - 1 )
=) x2 - 1
=) x2 - 1 - x( x - 1 )
=) 2 \(⋮\)x - 1
tự làm
a) Ta có: (x2 - 2x + 3) \(⋮\)(x - 1)
<=> [x(x - 1) - (x - 1) + 2] \(⋮\)(x - 1)
<=> [(x - 1)2 + 2] \(⋮\)(x - 1)
Do (x - 1)2 \(⋮\)(x - 1) => 2 \(⋮\)(x - 1)
=> (x - 1) \(\in\)Ư(2) = {1; -1; 2; -2}
Lập bảng :
x - 1 | 1 | -1 | 2 | -2 |
x | 2 | 0 | 3 | -1 |
Vậy ...
b) (3x - 1) \(⋮\)(x - 4)
<=> [3(x - 4) + 11] \(⋮\)(x - 4)
Do 3(x - 4) \(⋮\)(x - 4) => 11 \(⋮\)(x - 4)
=> (x - 4) \(\in\)Ư(11) = {1; -1; 11; -11}
Lập bảng:
x - 4 | 1 | -1 | 11 | -11 |
x | 5 | 3 | 15 | -7 |
vậy ...
c;d tương tự trên
a) \(\frac{18^4.3^2.8^3}{27^3.16^2}=\frac{\left(2.3^2\right)^4.3^2.\left(2^3\right)^3}{\left(3^3\right)^3.\left(2^4\right)^2}=\frac{2^4.2^9.3^8.3^2}{3^9.2^8}=\frac{2^{13}.3^{10}}{3^9.2^8}=3.2^5=96\)
b) \(\frac{35^5.9^3.8^5}{81^4.32^5}=\frac{35^5.\left(3^2\right)^3.\left(2^3\right)^5}{\left(3^4\right)^4.\left(2^5\right)^5}=\frac{35^5.3^6.2^{15}}{3^{16}.2^{25}}=\frac{35^5}{3^{10}.2^{10}}=\frac{35^5}{6^{10}}\)
c) \(\frac{48^5.18^2}{81^2.34^4}=\frac{\left(2^4.3\right)^5.\left(2.3^2\right)^2}{\left(3^4\right)^2.\left(2.17\right)^4}=\frac{2^{20}.3^5.2^2.3^4}{3^8.2^4.17^4}=\frac{2^{22}.3^9}{3^8.2^4.17^4}=\frac{2^{18}.3}{17^4}\)
d) \(\frac{54^7.27^3.16^2}{243^2.64^3}=\frac{\left(2.3^3\right)^7.\left(3^3\right)^3.\left(2^4\right)^2}{\left(3^5\right)^2.\left(2^6\right)^3}=\frac{2^7.3^{21}.3^9.2^8}{3^{10}.2^{18}}=\frac{2^{15}.3^{30}}{3^{10}.2^{18}}=\frac{3^{20}}{2^3}\)
\(\left(x-5\right)-27=18\)
\(x-5=45\)
\(x=50\)
vậy \(x=50\)
b) \(\left(3x-2^3\right).25=250\)
\(3x-8=10\)
\(3x=18\)
\(x=6\)
vậy \(x=6\)
c) \(108⋮x\)\(\Rightarrow x\inƯ\left(108\right)\) \(\Rightarrow x\in\left\{1;2;4;...;108\right\}\)
những ý sau làm tương tự
a)(x-5)-27=18
x-5=45
x=50
b)\(\left(3x-2^3\right).25=250\)
\(3x-2^3=10\)
\(3x=18\)
\(x=6\)