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Bài 2:
a) \(\left(x-3\right)^3+27=0\)
\(\Leftrightarrow\left(x-3\right)^3=0-27\)
\(\Leftrightarrow\left(x-3\right)^3=-27\)
\(\Leftrightarrow\left(x-3\right)^3=\left(-3\right)^3\)
\(\Leftrightarrow x-3=-3\)
\(\Leftrightarrow x=\left(-3\right)+3\)
\(\Leftrightarrow x=0\)
b) \(-125-\left(x+1\right)^3=0\)
\(\Leftrightarrow\left(x+1\right)^3=-125-0\)
\(\Leftrightarrow\left(x+1\right)^3=-125\)
\(\Leftrightarrow\left(x+1\right)^3=\left(-5\right)^3\)
\(\Leftrightarrow x+1=-5\)
\(\Leftrightarrow x=\left(-5\right)-1\)
\(\Leftrightarrow x=-6\)
c) \(\left(2x-\dfrac{1}{4}\right)^2-\dfrac{1}{16}=0\)
\(\Leftrightarrow\left(2x-\dfrac{1}{4}\right)^2=0+\dfrac{1}{16}\)
\(\Leftrightarrow\left(2x-\dfrac{1}{4}\right)^2=\dfrac{1}{16}\)
\(\Leftrightarrow\left(2x-\dfrac{1}{4}\right)^2=\left(\dfrac{1}{4}\right)^2\)
\(\Leftrightarrow2x-\dfrac{1}{4}=\dfrac{1}{4}\)
\(\Leftrightarrow2x=\dfrac{1}{4}+\dfrac{1}{4}\)
\(\Leftrightarrow2x=\dfrac{1}{2}\)
\(\Leftrightarrow x=\dfrac{1}{2}:2\)
\(\Leftrightarrow x=\dfrac{1}{4}\)
d) \(2^x+2^{x+1}=24\)
\(\Leftrightarrow2^x+2^x.2=24\)
\(\Leftrightarrow2^x\left(1+2\right)=24\)
\(\Leftrightarrow2^x.3=24\)
\(\Leftrightarrow2^x=24:3\)
\(\Leftrightarrow2^x=8\)
\(\Leftrightarrow2^x=2^3\)
\(\Rightarrow x=3\)
e) \(\left|x+\dfrac{1}{5}\right|-\dfrac{1}{2}=1\)
\(\Leftrightarrow\left|x+\dfrac{1}{5}\right|=1+\dfrac{1}{2}\)
\(\Leftrightarrow\left|x+\dfrac{1}{5}\right|=\dfrac{3}{2}\)
\(\Leftrightarrow\left[{}\begin{matrix}x+\dfrac{1}{5}=-\dfrac{3}{2}\\x+\dfrac{1}{5}=\dfrac{3}{2}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{17}{10}\\x=\dfrac{13}{10}\end{matrix}\right.\)
g) \(\left|x-3\right|+2x=10\)
\(\Leftrightarrow\left|x-3\right|=10-2x\)
\(\Leftrightarrow\left|x-3\right|=2.5-2x\)
\(\Leftrightarrow\left|x-3\right|=2\left(5-x\right)\)
(không chắc có nên làm tiếp câu g không, thấy đề cứ là lạ, có j sai sai...)
Bài 1:
a) \(2^7+2^9⋮10\)
Ta có: \(2^7+2^9=2^{4.1}.2^3+2^{4.2}.2\)
\(\Leftrightarrow\overline{A6}.2^3+\overline{B6}.2\)
\(\Leftrightarrow\overline{A6}.8+\overline{B6}.2\)
\(\Leftrightarrow\overline{C8}+\overline{D2}\)
\(\Leftrightarrow\overline{E0}\)
Mà \(\overline{E0}⋮10\) \(\Rightarrow2^7+2^9⋮10\)
b) \(8^{24}.25^{10}⋮2^{36}.5^{20}\)
Ta có: \(8^{24}.25^{10}=\left(2^3\right)^{24}.\left(5^2\right)^{10}\)
\(\Leftrightarrow2^{72}.5^{20}\)
Do \(2^{72}⋮2^{36}\) và \(5^{20}⋮5^{20}\) \(\Rightarrow8^{24}.25^{10}⋮2^{36}.5^{20}\)
c) \(3^{10}+3^{12}⋮30\)
Ta có: \(3^{10}+3^{12}=3^{4.2}.3^2+3^{4.3}\)
\(\Leftrightarrow\overline{A1}.3^2+\overline{B1}\)
\(\Leftrightarrow\overline{A1}.9+\overline{B1}\)
\(\Leftrightarrow\overline{C9}+\overline{B1}\)
\(\Leftrightarrow\overline{D0}⋮10\)
(Chứng minh chia hết cho 10 rồi chứng minh chia hết cho 3, mình chưa tìm được cách làm, chờ chút)
a) 169 . ( 3x - 9.17 ) + 24 : 3 = 30
169 . ( 3x - 153 ) + 8 = 30
169 . ( 3x - 153 ) = 30 - 8
169 . ( 3x - 153 ) = 22
3x - 153 = 22 : 169
3x - 153 = \(\frac{22}{169}\)
3x = \(\frac{22}{169}+153\)
3x = \(\frac{25879}{169}\)
x = \(\frac{25879}{169}:3\)
x = \(\frac{25879}{507}\)
Vậy \(x=\frac{25879}{507}\)
b) \(\left(\frac{4}{5}:\frac{6}{5}+\frac{1}{5}:\frac{1}{x}\right).30-26=54\)
\(\left(\frac{2}{3}+\frac{1}{5}.x\right).30=54+26\)
\(\left(\frac{2}{3}+\frac{1}{5}.x\right).30=80\)
\(\left(\frac{2}{3}+\frac{1}{5}.x\right)=80:30\)
\(\frac{2}{3}+\frac{1}{5}.x=\frac{8}{3}\)
\(\frac{1}{5}.x=\frac{8}{3}-\frac{2}{3}\)
\(\frac{1}{5}.x=2\)
\(x=2:\frac{1}{5}\)
\(x=10\)
Vậy \(x=10\)
c) \(\frac{1}{2}-\left(6\frac{5}{9}+x-\frac{117}{18}\right):12\frac{1}{9}=0\)
\(\frac{1}{2}-\left(\frac{59}{9}+x-\frac{117}{18}\right):\frac{109}{9}=0\)
\(\frac{1}{2}.\left(\frac{59}{9}-\frac{117}{18}+x\right).\frac{9}{109}=0\)
\(\frac{1}{2}.\left(\frac{1}{18}+x\right).\frac{9}{109}=0\)
\(\frac{1}{2}.\left(\frac{1}{18}+x\right)=0:\frac{9}{109}\)
\(\frac{1}{2}.\left(\frac{1}{18}+x\right)=0\)
\(\frac{1}{18}+x=0:\frac{1}{2}\)
\(\frac{1}{18}+x=0\)
\(x=0-\frac{1}{18}\)
\(x=\frac{-1}{18}\)
Vậy \(x=\frac{-1}{18}\)
d) 720 : [ 41 - ( 2x - 5 ) ] = 210
41 - 2x + 5 = 720 : 210
41 + 5 - 2x = \(\frac{24}{7}\)
46 - 2x = \(\frac{24}{7}\)
2x = \(46-\frac{24}{7}\)
2x = \(\frac{298}{7}\)
x = \(\frac{298}{7}:2\)
x = \(\frac{149}{7}\)
Vậy \(x=\frac{149}{7}\)
a) \(\left(2x+1\right)^3=9.81\)
\(\Rightarrow\left(2x+1\right)^3=729\)
\(\Rightarrow\left(2x+1\right)^3=9^3\)
\(\Rightarrow2x+1=9\)
\(\Rightarrow2x=9-1\)
\(\Rightarrow2x=8\)
\(\Rightarrow x=8:2\)
\(\Rightarrow x=4\)
b)\(5^x+5^{x+2}=650\)
\(\Rightarrow5^x+5^x.5^2=650\)
\(\Rightarrow5^x\left(1+25\right)=650\)
\(\Rightarrow5^x.26=650\)
\(\Rightarrow5^x=25\)
\(\Rightarrow x=2\)
c)\(2.3^{2x-1}=54\)
\(\Rightarrow2.3^{2x-1}=54\)
\(\Rightarrow2.\left(3^2\right)^x:3^1=54\)
\(\Rightarrow2.9^x:3=54\)
\(\Rightarrow9^x=81\)
\(\Rightarrow x=2\)
a) \(2^x+5=21\)
\(\Rightarrow2^x=21-5=16\Rightarrow2^x=2^4\)
Vậy x = 4
b) \(2^x-1+3^2=5^2+2.5\)
\(\Rightarrow2^x-1+9=35\)
\(\Rightarrow2^x=35-9+1=27\)
Vậy x không có giá trị
c;d;e;f làm tương tự
a) Ta có: \(\frac{2}{3}x-\frac{1}{2}=\frac{1}{10}\)
\(\Leftrightarrow x\cdot\frac{2}{3}=\frac{1}{10}+\frac{1}{2}=\frac{6}{10}\)
hay \(x=\frac{6}{10}:\frac{2}{3}=\frac{6}{10}\cdot\frac{3}{2}=\frac{18}{20}=\frac{9}{10}\)
Vậy: \(x=\frac{9}{10}\)
b) Ta có: \(5\frac{4}{7}:x=13\)
\(\Leftrightarrow\frac{39}{7}:x=13\)
\(\Leftrightarrow x=\frac{39}{7}:13=\frac{39}{7}\cdot\frac{1}{13}=\frac{3}{7}\)
Vậy: \(x=\frac{3}{7}\)
c) Ta có: \(\left(2\frac{4}{5}x-50\right):\frac{2}{3}=51\)
\(\Leftrightarrow\frac{14}{5}x-50=51\cdot\frac{2}{3}=34\)
\(\Leftrightarrow x\cdot\frac{14}{5}=84\)
\(\Leftrightarrow x=84:\frac{14}{5}=84\cdot\frac{5}{14}=\frac{420}{14}=30\)
Vậy: x=30
d) Ta có: \(\frac{2}{3}+\frac{1}{3}:x=\frac{3}{5}\)
\(\Leftrightarrow\frac{1}{3}:x=\frac{3}{5}-\frac{2}{3}=\frac{-1}{15}\)
hay \(x=\frac{1}{3}:\frac{-1}{15}=\frac{1}{3}\cdot\left(-15\right)=\frac{-15}{3}=-5\)
Vậy: x=-5
e) Ta có: \(8\frac{2}{3}:x-10=-8\)
\(\Leftrightarrow\frac{26}{3}:x=2\)
hay \(x=\frac{26}{3}:2=\frac{26}{3}\cdot\frac{1}{2}=\frac{26}{6}=\frac{13}{3}\)
Vậy: \(x=\frac{13}{3}\)
g) Ta có: \(x+30\%=-1.3\)
\(\Leftrightarrow x+\frac{3}{10}=\frac{-13}{10}\)
hay \(x=\frac{-13}{10}-\frac{3}{10}=\frac{-16}{10}=\frac{-8}{5}\)
Vậy: \(x=\frac{-8}{5}\)
i) Ta có: \(3\frac{1}{3}x+16\frac{3}{4}=-13.25\)
\(\Leftrightarrow x\cdot\frac{10}{3}+\frac{67}{4}=-\frac{53}{4}\)
\(\Leftrightarrow x\cdot\frac{10}{3}=\frac{-53}{4}-\frac{67}{4}=-30\)
\(\Leftrightarrow x=-30:\frac{10}{3}=-30\cdot\frac{3}{10}=\frac{-90}{10}=-9\)
Vậy: x=-9
k) Ta có: \(\left(2\frac{4}{5}x-50\right):\frac{2}{3}=51\)
\(\Leftrightarrow x\cdot\frac{14}{5}-50=51\cdot\frac{2}{3}=34\)
\(\Leftrightarrow x\cdot\frac{14}{5}=34+50=84\)
hay \(x=84:\frac{14}{5}=84\cdot\frac{5}{14}=30\)
Vậy: x=30
m) Ta có: \(\left|2x-1\right|=\left(-4\right)^2\)
\(\Leftrightarrow\left|2x-1\right|=16\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-1=16\\2x-1=-16\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=17\\2x=-15\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\frac{17}{2}\\x=\frac{-15}{2}\end{matrix}\right.\)
Vậy: \(x\in\left\{\frac{17}{2};\frac{-15}{2}\right\}\)
\(a,2x-138=2^3:\left(-3\right)^2\)
\(\Rightarrow2x-138=8:9\)
\(\Rightarrow2x=\frac{8}{9}+138\)
\(\Rightarrow2x=\frac{1250}{9}\)
\(\Rightarrow x=\frac{626}{9}\)
\(10+2x=\left(-4\right)^5:\left(-4\right)^3\)
\(10+2x=-1024:\left(-64\right)\)
\(10+2x=16\)
\(2x=16-10\)
\(2x=6\)
\(x=6:2=3\)
a) \(\frac{5}{6}=\frac{x-1}{x}\)
\(5x=6x-6\)
\(6x-5x=6\)
\(x=6\)
các câu còn lại lm tương tự
hok tốt!!
b) \(\frac{1}{2}=\frac{x+1}{3x}\)
\(\Rightarrow1.3x=2.\left(x+1\right)\)
\(3x=2x+2\)
\(3x-2x=2\)
\(x=2\)
Vậy x=2
các câu khác bạn làm tương tự
\(2x+\frac{1}{4}=\frac{3}{2}\)
\(\Rightarrow2x=\frac{3}{2}-\frac{1}{4}=\frac{5}{4}\)
\(\Rightarrow x=\frac{5}{4}:2=\frac{5}{8}\)
\(\left(x-5\right)-\frac{1}{3}=\frac{2}{5}\)
\(\Rightarrow x-5=\frac{2}{5}+\frac{1}{3}=\frac{11}{15}\)
\(\Rightarrow x=\frac{11}{15}+5=5\frac{11}{15}\)
1) \(4\left(2x-1\right)^2-10=54\)
\(\Leftrightarrow4\left(2x-1\right)^2=64\)
\(\Leftrightarrow\left(2x-1\right)^2=16\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}2x-1=4\\2x-1=-4\end{array}\right.\)\(\Leftrightarrow\left[\begin{array}{nghiempt}x=\frac{5}{2}\\x=-\frac{3}{2}\end{array}\right.\)
2)\(5\left(3^{2x-1}+30\right)=165\)
\(\Leftrightarrow3^{2x-1}+30=33\)
\(\Leftrightarrow3^{2x-1}=3\)
\(\Leftrightarrow2x-1=1\)
\(\Leftrightarrow x=1\)