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7 tháng 10 2016
Theo bài ra , ta có :
\(\frac{x}{4}+\frac{x}{8}+\frac{x}{16}=\frac{x}{9}+\frac{x}{27}+\frac{x}{81}\)
\(\Rightarrow\frac{x}{4}+\frac{x}{8}+\frac{x}{16}-\frac{x}{9}-\frac{x}{27}-\frac{x}{81}=0\)
\(\Rightarrow x=0\)
Vậy \(x=0\)
19 tháng 9 2016
a, (x+1).3 = 2.2
=>3 x+3 =4
=> 3x=1
=> x=1/3
b, (x-2) .4 =(x+1).3
=>4x-8=3x+3
=>4x-3x=8+3
=>x=11
c, lam tg tu cau b
d, (x-1)(x+3)=(x+2)(x-2)
\(x^2\)+3x-x-3=\(x^2\)-2x+2x-4
x^2 +2x-3=x^2-4
x^2-x^2+2x=3-4
2x=-1
x=-0,5
22 tháng 10 2016
\(\frac{x+1}{2}=\frac{2}{3}\)
\(\Rightarrow3.\left(x+1\right)=2.2\)
\(\Rightarrow3x+3=4\)
\(\Rightarrow3x=4-3\)
\(\Rightarrow3x=1\)
\(\Rightarrow x=\frac{1}{3}\)
\(b,\frac{x-2}{3}=\frac{x+1}{4}\)
\(\Rightarrow4.\left(x-2\right)=3.\left(x+1\right)\)
\(\Rightarrow4x-8=3x+3\)
\(\Rightarrow4x-3x=3+8\)
\(\Rightarrow x=11\)
\(c,\frac{x-3}{x+5}=\frac{5}{7}\)
\(\Rightarrow7.\left(x-3\right)=5.\left(x+5\right)\)
\(\Rightarrow7x-21=5x+25\)
\(\Rightarrow7x-5x=25+21\)
\(\Rightarrow2x=46\)
\(\Rightarrow x=23\)
\(d,\frac{x-1}{x+2}=\frac{x-2}{x+3}\)
\(\Rightarrow\left(x-1\right)\left(x+3\right)=\left(x+2\right)\left(x-2\right)\)
\(\Rightarrow x^2+2x-3=x^2-4\)
\(\Rightarrow2x=-1\)
\(\Rightarrow x=-\frac{1}{2}\)
T
5 tháng 10 2018
Giải bài khó nhất =)
\(\frac{x+4}{2000}+\frac{x+3}{2001}=\frac{x+2}{2002}+\frac{x+1}{2003}\)
\(\Leftrightarrow\left(\frac{x+4}{2000}+1\right)+\left(\frac{x+3}{2001}+1\right)=\left(\frac{x+2}{2002}+1\right)+\left(\frac{x+1}{2003}+1\right)\)
\(\Leftrightarrow\frac{x+2004}{2000}+\frac{x+2004}{2001}=\frac{x+2004}{2002}+\frac{x+2004}{2003}\)
\(\Leftrightarrow\frac{x+2004}{2000}+\frac{x+2004}{2001}-\frac{x+2004}{2002}-\frac{x+2004}{2003}=0\)
\(\Leftrightarrow\left(x+2004\right)\left(\frac{1}{2000}+\frac{1}{2001}+\frac{1}{2002}+\frac{1}{2003}\right)=0\)
Do \(\frac{1}{2000}+\frac{1}{2001}+\frac{1}{2002}+\frac{1}{2003}\ne0\) nên \(x+2004=0\Leftrightarrow x=-2004\)
12 tháng 9 2020
a) \(\frac{2}{x-3}=\frac{5}{4}\)(ĐKXĐ : x khác 3)
=> \(2\cdot4=5\left(x-3\right)\)
=> \(8=5x-15\)
=> \(5x-15=8\)
=> \(5x=23\)=> x = 23/5 (tm)
b) \(\frac{x+1}{5}=\frac{4x-2}{3}\)
=> 3(x + 1) = 5(4x - 2)
=> 3x + 3 = 20x - 10
=> 3x + 3 - 20x + 10 = 0
=> 3x - 20x + 3 + 10 = 0
=> 3x - 20x = -13
=> -17x = -13
=> x = 13/17(tm)
2. a) Nếu đề như thế này : \(\frac{x}{2}=\frac{y}{3}=\frac{z}{5}\) và x - 2y + 2z = 10
=> \(\frac{x}{2}=\frac{2y}{6}=\frac{2z}{10}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có :
\(\frac{x}{2}=\frac{2y}{6}=\frac{2z}{10}=\frac{x-2y+2z}{2-6+10}=\frac{10}{6}=\frac{5}{3}\)
=> x = 5/3.2 = 10/3 , y = 5/3.3 = 5, z = 5/3.5 = 25/3 ( nên sửa lại đề bài này nhá)
b) Bạn tự làm
c) \(\frac{x}{y}=\frac{3}{5}\)=> \(\frac{x}{3}=\frac{y}{5}\)=> \(\frac{2x}{6}=\frac{3y}{15}\)
Áp dụng t/c dãy tỉ số bằng nhau ta có :
\(\frac{2x}{6}=\frac{3y}{15}=\frac{2x-3y}{6-15}=\frac{12}{-11}=-\frac{12}{11}\)
=> \(x=-\frac{12}{11}\cdot3=-\frac{36}{11},y=-\frac{12}{11}\cdot5=-\frac{60}{11}\)
d) Đặt x/3 = y/4 = k
=> x = 3k, y = 4k
Theo đề bài ta có => xy = 3k.4k = 12k2
=> 48 = 12k2
=> k2 = 48 : 12 = 4
=> k = 2 hoặc k = -2
Với k = 2 thì x = 3.2 = 6 , y = 4.2 = 8
Với k = -2 thì x = 3(-2) = -6 , y = 4(-2) = -8
12 tháng 9 2020
Bài 1.
a) \(\frac{2}{x-3}=\frac{5}{4}\)( ĐK : x khác 3 )
<=> 2.4 = ( x - 3 ).5
<=> 8 = 5x - 15
<=> 8 + 15 = 5x
<=> 23 = 5x
<=> 23/5 = x ( tmđk )
b) \(\frac{x+1}{5}=\frac{4x-2}{3}\)
<=> ( x + 1 ).3 = 5( 4x - 2 )
<=> 3x + 3 = 20x - 10
<=> 3x - 20x = -10 - 3
<=> -17x = -13
<=> x = 13/17
Bài 2.
a) \(\hept{\begin{cases}\frac{x}{2}=\frac{y}{3}=\frac{z}{5}\\x-2y+2z=10\end{cases}}\Leftrightarrow\hept{\begin{cases}\frac{x}{2}=\frac{2y}{6}=\frac{2z}{10}\\x-2y+2z=10\end{cases}}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có :
\(\frac{x}{2}=\frac{2y}{6}=\frac{2z}{10}=\frac{x-2y+2z}{2-6+10}=\frac{10}{6}=\frac{5}{3}\)
\(\Rightarrow\hept{\begin{cases}x=\frac{5}{3}\cdot2=\frac{10}{3}\\y=\frac{5}{3}\cdot3=5\\z=\frac{5}{3}\cdot5=\frac{25}{3}\end{cases}}\)
b) \(\hept{\begin{cases}\frac{x}{2}=\frac{y}{5}\\\frac{z}{4}=\frac{y}{6}\\x-y+z=20\end{cases}}\Leftrightarrow\hept{\begin{cases}\frac{x}{2}\times\frac{1}{6}=\frac{y}{5}\times\frac{1}{6}\\\frac{z}{4}\times\frac{1}{5}=\frac{y}{6}\times\frac{1}{5}\\x-y+z=20\end{cases}}\Leftrightarrow\hept{\begin{cases}\frac{x}{12}=\frac{y}{30}\\\frac{z}{20}=\frac{y}{30}\\x-y+z=20\end{cases}}\Rightarrow\hept{\begin{cases}\frac{x}{12}=\frac{y}{30}=\frac{z}{20}\\x-y+z=20\end{cases}}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có :
\(\frac{x}{12}=\frac{y}{30}=\frac{z}{20}=\frac{x-y+z}{12-30+20}=\frac{20}{2}=10\)
\(\Rightarrow\hept{\begin{cases}x=10\cdot12=120\\y=10\cdot30=300\\z=10\cdot20=200\end{cases}}\)
c) \(\hept{\begin{cases}\frac{x}{y}=\frac{3}{5}\\2x-3y=12\end{cases}}\Leftrightarrow\hept{\begin{cases}\frac{x}{3}=\frac{y}{5}\\2x-3y=12\end{cases}}\Leftrightarrow\hept{\begin{cases}\frac{2x}{6}=\frac{3y}{15}\\2x-3y=12\end{cases}}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có :
\(\frac{2x}{6}=\frac{3y}{15}=\frac{2x-3y}{6-15}=\frac{12}{-9}=-\frac{4}{3}\)
\(\Rightarrow\hept{\begin{cases}x=-\frac{4}{3}\cdot3=-4\\y=-\frac{4}{3}\cdot5=-\frac{20}{3}\end{cases}}\)
d) Đặt \(\frac{x}{3}=\frac{y}{4}=k\Rightarrow\hept{\begin{cases}x=3k\\y=4k\end{cases}}\)
xy = 48
<=> 3k.4k= 48
<=> 12k2 = 48
<=> k2 = 4
<=> k = ±2
+) Với k = 2 => \(\hept{\begin{cases}x=3\cdot2=6\\y=4\cdot2=8\end{cases}}\)
+) Với k = -2 => \(\hept{\begin{cases}x=3\cdot\left(-2\right)=-6\\y=4\cdot\left(-2\right)=-8\end{cases}}\)
14 tháng 9 2017
\(a,\frac{-1}{2}+\left(x-3\right):\frac{-1}{2}=-1\frac{2}{3}.\)
\(\Rightarrow\left(x-3\right):\frac{-1}{2}=-1\frac{2}{3}-\frac{-1}{2}=\frac{-7}{6}\)
\(\Rightarrow x-3=\frac{-7}{6}\cdot\frac{-1}{2}=\frac{7}{12}\)
\(\Rightarrow x=\frac{7}{12}+3=3\frac{7}{12}\)
\(b.2,25+\frac{3}{2}:\left(x-5\right)=2\frac{1}{2}\)
\(\Rightarrow\frac{3}{2}:\left(x-5\right)=2\frac{1}{2}-2,25=\frac{1}{4}\)
\(\Rightarrow x-5=\frac{3}{2}:\frac{1}{4}=6\)
\(\Rightarrow x=6+5=11\)
\(c,\left(\frac{1}{3}-x\right)^2=\frac{1}{4}=\left(\frac{1}{2}\right)^2=\left(-\frac{1}{2}\right)^2\)
\(\Rightarrow\orbr{\begin{cases}\frac{1}{3}-x=\frac{1}{2}\\\frac{1}{3}-x=-\frac{1}{2}\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{1}{3}-\frac{1}{2}=-\frac{1}{6}\\x=\frac{1}{3}-\frac{-1}{2}=\frac{5}{6}\end{cases}}\)
\(d,\frac{3}{2}+\frac{x-1}{3}=1\)
\(\Rightarrow\frac{x-1}{3}=1-\frac{3}{2}=-\frac{1}{2}\)
\(\Rightarrow x-1=-\frac{1}{2}\cdot3=-\frac{3}{2}\)
\(\Rightarrow x=-\frac{3}{2}+1=\frac{1}{2}\)
\(e,-\frac{6}{8}+\frac{x}{12}=\frac{5}{6}\)
\(\Rightarrow\frac{x}{12}=\frac{5}{6}-\frac{-6}{8}=\frac{19}{12}\)
\(\Rightarrow x=19\)
\(g,\frac{1}{2}-\frac{1}{3}\left(x-2\right)=-\frac{2}{3}\)
\(\Rightarrow-\frac{1}{3}\left(x-2\right)=-\frac{2}{3}-\frac{1}{2}=-\frac{7}{6}\)
\(\Rightarrow x-2=\frac{-7}{6}:\frac{-1}{3}=\frac{7}{2}\)
\(\Rightarrow x=\frac{7}{2}+2=2\frac{7}{2}\)
\(h,\frac{5}{2}\left(x+1\right)-\frac{1}{2}=3\frac{1}{2}\)
\(\Rightarrow\frac{5}{2}\left(x+1\right)=3\frac{1}{2}-\frac{1}{2}=3\)
\(\Rightarrow x+1=3:\frac{5}{2}=\frac{6}{5}\)
\(\Rightarrow x=\frac{6}{5}-1=\frac{1}{5}\)
\(k,\frac{x}{3}-\frac{1}{2}=-2\left(x+1\right)+3\)
\(\Rightarrow x\cdot\frac{1}{3}-\frac{1}{2}=-2x-2+3\)
\(\Rightarrow\frac{1}{3}x+2x=-2+3+\frac{1}{2}\)
\(\Rightarrow\frac{7}{3}x=\frac{3}{2}\Rightarrow x=\frac{3}{2}:\frac{7}{2}=\frac{3}{7}\)
4 tháng 10 2016
a) \(\frac{x+7}{x+4}=\frac{2}{5}\)
\(\Rightarrow5\left(x+7\right)=2\left(x+4\right)\)
\(\Rightarrow5x+35-2x-8=0\)
\(\Rightarrow3x=-27\)
\(\Rightarrow x=-9\)
b) \(\frac{2x-3}{2}=\frac{50}{2x-3}\)
\(\Rightarrow\left(2x-3\right)^2=100\)
\(\Rightarrow\left[\begin{array}{nghiempt}2x-3=10\\2x-3=-10\end{array}\right.\)\(\Rightarrow\left[\begin{array}{nghiempt}x=\frac{13}{2}\\x=-\frac{7}{2}\end{array}\right.\)
c) \(\frac{x+1}{x-3}=\frac{x+3}{x+2}\)
\(\Rightarrow\left(x+1\right)\left(x+2\right)=\left(x-3\right)\left(x+3\right)\)
\(\Leftrightarrow x^2+3x+2=x^2-9\)
\(\Leftrightarrow3x=-11\)
\(\Leftrightarrow x=-\frac{11}{3}\)
9 tháng 6 2016
a) \(\left(x-3^2\right)^3=\left(3^3\right)^2=\left(3^2\right)^3\)
=> x - 32 = 32
=> x = 32 + 32 = 2. 32 = 18
b) => 15x = 8y => \(\frac{y}{15}=\frac{x}{8}=\frac{y-x}{15-8}=\frac{21}{7}=3\)
=> y = 30 ; x = 24
c) => (x - 3). 7 = (x + 5). 5
=> 7x - 21 = 5x + 5 => 7x - 5x = 5 + 21
=> 2x = 26 => x = 13
d) => (x - 1). (x + 3) = (x + 2). (x - 2)
=> x. (x + 3) - (x + 3) = x. (x - 2) + 2.(x - 2)
=> x2 + 3x - x - 3 = x2 - 2x + 2x - 4
=> 2x - 3 = -4 => 2x = -1 => x = -0,5
9 tháng 6 2016
a) \(\left(x-3^2\right)^3=\left(3^3\right)^2=\left(3^2\right)^3\)
\(\Rightarrow x-3^2=3^2\)
\(\Rightarrow x=3^2+3^2=9+9=18\)
Vậy x = 18
b) \(\frac{3x}{2}=\frac{4y}{5}=\frac{4y-3x}{5-2}=\frac{\left(3y-3x\right)+y}{3}=\frac{3\left(y-x\right)+y}{3}=\frac{63+y}{3}=\frac{y}{3}+21\)
Ta có: \(\frac{4y}{5}=\frac{y}{3}+21\)
\(\Rightarrow\frac{4y}{5}-\frac{y}{3}=21\)
\(\Rightarrow\frac{12y-5y}{15}=21\)
\(\Rightarrow7y=21.15=315\)
\(\Rightarrow y=315:7=45\)
Thay y = 45, ta đc :
\(\frac{3x}{2}=\frac{4.45}{5}=\frac{180}{5}=36\)
\(\Rightarrow3x=36.2=72\)
\(\Rightarrow x=72:3=24\)
Vậy x = 24, y = 45.
c, \(\frac{x-3}{x+5}=\frac{5}{7}\)
\(\Rightarrow\frac{x+5-8}{x+5}=\frac{5}{7}\)
\(\Rightarrow1+\frac{8}{x+5}=\frac{5}{7}\)
\(\Rightarrow\frac{8}{x+5}=-\frac{2}{7}\)
\(\Rightarrow x+5=8:-\frac{2}{7}=-28\)
\(\Rightarrow x=-28-5=-33\)
Vậy x = -33.
d) \(\frac{x-1}{x+2}=\frac{x-2}{x+3}\)
\(\Rightarrow\left(x-1\right)\left(x+3\right)=\left(x+2\right)\left(x-2\right)\)
\(\Rightarrow x\left(x+3\right)-\left(x+3\right)=x\left(x-2\right)+2\left(x-2\right)\)
\(\Rightarrow x^2+3x-x-3=x^2-2x+2x-4\)
\(\Rightarrow2x-3=-4\)
\(\Rightarrow2x=-1\)
\(\Rightarrow x=-\frac{1}{2}\)
Vậy \(x=-\frac{1}{2}\)
\(\frac{2}{x-3}=\frac{3}{x+2}\)\(\Rightarrow2\left(x+2\right)=3\left(x-3\right)\)\(\Rightarrow2x+4=3x-9\)\(\Rightarrow0=x-13\Rightarrow x=13\)
\(\Rightarrow2\left(x+2\right)=3\left(x-3\right)\)
=>2x+4=3x - 9
=>x=13