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a)437+(248-x)=635
248-x=635-437=198
x=248-198=50
b)5.(x+27)=465
x+27=465/5=93
x=93-27=66
c)3.(x+3)=30
x+3=30:3=10
x=10-3=7
d)8x-9=31
8x=31-9=22
x=22/8=11/4
e)7x-9=26
7x=26+9=35
x=35:7=5
g)76-3.(x+5)=16
3.(x+5)=76-16=60
x+5=60/3=20
x=15
a) \(\left(19x+2\times5^2\right):14=\left(13-8\right)^2-4^2\)
\(\Rightarrow\left(19x+50\right):14=5^2-4^2=25-16=9\)
\(\Rightarrow19x+50=126\)
\(\Rightarrow19x=76\Rightarrow x=4\)
Vậy x = 4
b) \(2\times3^2=10\times3^{12}+8\times27^4\)
\(\Rightarrow2\times3^2=10\times\left(3^3\right)^4+8\times27^4\)
\(\Rightarrow2\times3^2=27^4\times\left(10+8\right)\)
\(\Rightarrow18=27^4\times18\)
\(\Rightarrow27^4\times18-18=0\Rightarrow18\times\left(27^4-1\right)=0\)
=> Không thấy biến x đâu cả
c) Ta thấy 33 = 27
\(\Rightarrow3^{2x-5}=3^3\Rightarrow2x-5=3\Rightarrow2x=8\Rightarrow x=4\)
Vậy x = 4
d) \(3^{x+1}-x=80\Rightarrow3^{x+1}=81\)
Ta thấy 34 = 81
\(\Rightarrow3^{x+1}=3^4\Rightarrow x+1=4\Rightarrow x=3\)
Vậy x = 3
=> (1+2X-1)x (2x-1+1)/4=225
=> 2x+2x/4=225
=> 4x^2/4=225
=> x^2= 225
=> x=15
cái ^ là mũ nha bạn
chúc bn hok tốt
`Answer:`
a. Tổng: \([\left(2x-1\right)-1]:2+1=x\) số hạng
Ta có: \(1+3+5+7+9+...+\left(2x-1\right)=225\)
\(\Rightarrow x.\left(2x-1+1\right):2=225\)
\(\Leftrightarrow2x^2:2=225\)
\(\Leftrightarrow x^2=225\)
\(\Leftrightarrow x=15\)
b. Mình sửa đề nhé: \(2^x+2^{x+1}+2^{x+2}+2^{x+3}+...+2^{x+2015}=2^{2019}-8\)
\(\Rightarrow2^x.\left(1+2+2^2+...+2^{2015}\right)=2^{2019}-8\)
Ta đặt \(K=1+2+2^2+...+2^{2015}\)
\(\Rightarrow2^x.K=2^{2019}-8\)
\(\Rightarrow2K=2.\left(1+2+2^2+...+2^{2015}\right)\)
\(\Rightarrow2K=2+2^2+2^3+...+2^{2015}+2^{2016}\)
\(\Rightarrow2K-K=\left(2+2^2+2^3+...+2^{2015}+2^{2016}\right)-\left(1+2+2^2+...+2^{2015}\right)\)
\(\Rightarrow K=2^{2016}-1\)
\(\Rightarrow2^x.\left(2^{2016}-1\right)=2^{2019}-8\)
\(\Rightarrow2^{x+2016}-2^x=2^{2019}-2^3\)
\(\Rightarrow\hept{\begin{cases}x+2016=2019\\x=3\end{cases}}\Rightarrow x=3\)
Bài 1:
a, \(\left(x-2\right)^2=9\)
\(\Rightarrow x-2\in\left\{-3;3\right\}\Rightarrow x\in\left\{-1;5\right\}\)
b, \(\left(3x-1\right)^3=-8\)
\(\Rightarrow3x-1=-2\Rightarrow3x=-1\)
\(\Rightarrow x=-\dfrac{1}{3}\)
c, \(\left(x+\dfrac{1}{2}\right)^2=\dfrac{1}{16}\)
\(\Rightarrow x+\dfrac{1}{2}\in\left\{-\dfrac{1}{4};\dfrac{1}{4}\right\}\)
\(\Rightarrow x\in\left\{-\dfrac{3}{4};-\dfrac{1}{4}\right\}\)
d, \(\left(\dfrac{2}{3}\right)^x=\dfrac{4}{9}\)
\(\Rightarrow\left(\dfrac{2}{3}\right)^x=\left(\dfrac{2}{3}\right)^2\)
Vì \(\dfrac{2}{3}\ne\pm1;\dfrac{2}{3}\ne0\) nên \(x=2\)
e, \(\left(\dfrac{1}{2}\right)^{x-1}=\dfrac{1}{16}\)
\(\Rightarrow\left(\dfrac{1}{2}\right)^{x-1}=\left(\dfrac{1}{2}\right)^4\)
Vì \(\dfrac{1}{2}\ne\pm1;\dfrac{1}{2}\ne0\) nên \(x-1=4\Rightarrow x=5\)
f, \(\left(\dfrac{1}{2}\right)^{2x-1}=8\) \(\Rightarrow\left(\dfrac{1}{2}\right)^{2x-1}=\left(\dfrac{1}{2}\right)^{-3}\) Vì \(\dfrac{1}{2}\ne\pm1;\dfrac{1}{2}\ne0\) nên \(2x-1=-3\) \(\Rightarrow2x=-2\Rightarrow x=-1\) Chúc bạn học tốt!!!
c/ 2x - 1 = \(5^{98}:5^{96}\)
2x - 1 = \(5^2\) = 25
2x = 25 + 1 = 26
x = 26 : 2
x = 13
d/ 7x + 3 = \(3^5.2^3.9\)
7x + 3 = \(3^5.3^2.8=3^7.8=2187.8\)
7x + 3 = \(17496\)
7x = 17496 - 3 = 17493
x = 17493 : 7
x = 2499
e/\(2^{2x+6}=1\)
\(2^{2x+6}=2^0\)
2x + 6 = 0
2x = 0 - 6 = - 6
x = - 6 : 2
x = - 3
j/ \(2^x=8\)
\(2^x=2^3\)
x = 3
g/ \(2^x:2^3=16\)
\(2^{x-3}=2^4\)
x - 3 = 4
x = 4 + 3
x = 7
h/ \(2^x+2^{x+1}+2^{x+2}=56\)
\(2^x\left(1+2+2^2\right)\) = 56
\(2^x.7=56\)
\(2^x=56:7\)
\(2^x=8\)
\(2^x=2^3\)
x = 3
Bài a, b thiên phong giải r, mk chỉ làm những bài còn lại thôi. Chúc bạn học tốt!!!
a. \(\left(x+8\right)⋮\left(x+4\right)\)
\(\Rightarrow\left(x+4\right)+4⋮\left(x+4\right)\)
Mà \(\left(x+4\right)⋮\left(x+4\right)\)
\(\Rightarrow4⋮\left(x+4\right)\)
\(\Rightarrow x+4\in\text{Ư} \left(4\right)=\left\{1;2;4\right\}\)
Ta có 3 trường hợp :
TH1 : \(x+4=1\Rightarrow x\notin N\) ( Loại )
TH2 : \(x+4=2\Rightarrow x\notin N\)(Loại )
TH3 : \(x+4=4\Rightarrow x=0\)
Vậy x = 0
a,Vì : \(x+8⋮x+2\)
Mà : \(x+2⋮x+2\)
\(\Rightarrow\left(x+8\right)-\left(x+2\right)⋮x+2\Rightarrow x+8-x-2⋮x+2\)
\(\Rightarrow6⋮x+2\Rightarrow x+2\inƯ\left(6\right)\)
Mà : \(Ư\left(6\right)=\left\{1;2;3;6\right\}\) ; \(x+2\ge2\Rightarrow x+2\in\left\{2;3;6\right\}\)
\(\Rightarrow x\in\left\{0;1;4\right\}\)
Vậy ...
b,Ta có : \(2y+7⋮y-1\) ; \(y-1⋮y-1\Rightarrow2\left(y-1\right)⋮y-1\Rightarrow2y-2⋮y-1\)
\(\Rightarrow\left(2y+7\right)-\left(2y-2\right)⋮y-1\Rightarrow2y+7-2y+2⋮y-1\)
\(\Rightarrow9⋮y-1\Rightarrow y-1\in\left\{1;3;9\right\}\Rightarrow y\in\left\{2;4;10\right\}\)
Vậy ...
c, Vì : \(x\in N\Rightarrow x-5\in N\)
\(y\in N\Rightarrow y+3\in N\left(y+3\ge3\right)\)
\(\Rightarrow x-5,y+3\inƯ\left(7\right)\)
Mà : \(Ư\left(7\right)=\left\{1;7\right\};y+3\ge3\)
\(\Rightarrow x-5=1\Rightarrow x=6;y+3=7\Rightarrow y=4\)
Vậy ...
c) pt <=> \(x-\frac{21}{5}=\frac{23}{7}< =>x=\frac{23}{7}+\frac{21}{5}=\frac{262}{35}\)
vậy x = \(\frac{262}{35}\)
d) \(x-\frac{3}{4}=\frac{51}{8}< =>x=\frac{51}{8}+\frac{3}{4}=\frac{57}{8}\)
vậy x = \(\frac{57}{8}\)
e) pt <=> \(\frac{7}{8}:x=\frac{7}{2}< =>\frac{7}{8}.\frac{1}{x}=\frac{7}{2}< =>\frac{7}{8x}=\frac{7}{2}< =>56x=14< =>x=\frac{14}{56}=\frac{1}{4}\)
vậy x = \(\frac{1}{4}\)
a) pt <=> \(x+\frac{11}{4}=\frac{17}{3}< =>x=\frac{17}{3}-\frac{11}{4}=\frac{35}{12}\)
vậy x = \(\frac{35}{12}\)
b) pt <=> \(\frac{x.7}{2}=\frac{19}{4}< =>x=\frac{19.2}{4.7}=\frac{38}{28}=\frac{19}{14}\)
vậy x = \(\frac{19}{14}\)
Bài 1
xy=2 => x=1 ; y=2 và ngược lại
xy=5 => x=1 ; y=5 và ngược lại
a) x = 4
b) x = 7
c) x = 2
d) x = 5
e) x = 2
f) x= 1