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KT
13 tháng 2 2018
a) \(\frac{x+1}{4}-\frac{x+2}{5}+\frac{x+4}{7}-\frac{x+5}{8}+\frac{x+7}{10}-\frac{x+9}{12}=0\)
\(\Leftrightarrow\)\(\frac{x+1}{4}-1-\frac{x+2}{5}+1+\frac{x+4}{7}-1-\frac{x+5}{8}+1+\frac{x+7}{10}-1-\frac{x+9}{12}+1=0\)
\(\Leftrightarrow\)\(\frac{x-3}{4}-\frac{3-x}{5}+\frac{x-3}{7}-\frac{3-x}{8}+\frac{x+3}{10}-\frac{3-x}{12}=0\)
\(\Leftrightarrow\)\(\frac{x-3}{4}+\frac{x-3}{5}+\frac{x-3}{7}+\frac{x-3}{8}+\frac{x-3}{10}+\frac{x-3}{12}=0\)
\(\Leftrightarrow\)\(\left(x-3\right)\left(\frac{1}{4}+\frac{1}{5}+\frac{1}{7}+\frac{1}{8}+\frac{1}{10}+\frac{1}{12}\right)=0\)
Vì \(\frac{1}{4}+\frac{1}{5}+\frac{1}{7}+\frac{1}{8}+\frac{1}{10}+\frac{1}{12}\ne0\)
\(\Rightarrow\)\(x-3=0\)
\(\Leftrightarrow\)\(x=3\)
Vậy...
b) \(\frac{x}{2004}+\frac{x+1}{2005}+\frac{x+2}{2006}+\frac{x+3}{2007}=4\)
\(\Leftrightarrow\)\(\frac{x}{2004}-1+\frac{x+1}{2005}-1+\frac{x+2}{2006}-1+\frac{x+3}{2007}-1=0\)
\(\Leftrightarrow\)\(\frac{x-2004}{2004}+\frac{x-2004}{2005}+\frac{x-2004}{2006}+\frac{x-2004}{2007}=0\)
\(\Leftrightarrow\)\(\left(x-2004\right)\left(\frac{1}{2004}+\frac{1}{2005}+\frac{1}{2006}+\frac{1}{2007}\right)=0\)
Vì \(\frac{1}{2004}+\frac{1}{2005}+\frac{1}{2006}+\frac{1}{2007}\ne0\)
\(\Rightarrow\)\(x-2004=0\)
\(\Leftrightarrow\)\(x=2004\)
Vậy...
AD
1 tháng 7 2018
a/ (x-1)2 - (x+1)2 = 3
<=> (x-1-x-1)(x-1+x+1) = 3
<=> - 2 . 2x = 3
<=> -4x = 3 <=> x = -3/4
KL: x = -3/4
b/ (x-2)(x+2) - (x-3) ^2 = 5x - 1
<=> x2 - 4 - x2 + 6x - 9 = 5x - 1
<=> 6x - 5x = -1 + 4 + 9
<=> x = 12
KL: x= 12
c/ x(x-2) - (x+3)2 - x = 4
<=> x2 - 2x - x2 - 6x - 9 - x = 4
<=> -9x = 4 + 9
<=> x = -13/9
KL: x= -13/9
d/ 6x(x-1) - 5(x-2)2 - x(x - 3) = 4
<=> 6x2 - 6x - 5(x2 - 4x + 4) - x2 - 3x = 4
<=> 6x2 - 6x - 5x2 + 20x - 20 -x2 - 3x = 4
<=> 11x = 24
<=> x = 24/11
KL: x = 24/11
TT
1 tháng 7 2018
a)
\(\left(x-1\right)^2-\left(x+1\right)^2=3\\ \Leftrightarrow-2.2x=3\\ \Leftrightarrow-4x=3\\ \Leftrightarrow x=-\dfrac{4}{3}\)
Vậy...
b)
\(\left(x-2\right)\left(x+2\right)-\left(x-3\right)^2=5x-1\\ \Leftrightarrow x^2-4-\left(x^2-6x+9\right)=5x-1\\ \Leftrightarrow x^2-4-x^2+6x-9=5x-1\\ \Leftrightarrow-13+6x=5x-1\\ \Leftrightarrow6x-5x=-1+13\\ \Leftrightarrow x=12\)
Vậy...
a)-x/2=1/-2
-x/2=-1/2
=>-x=-1
Vậy x=1
b)\(\frac{x}{2}+\frac{x}{3}+\frac{x}{4}+\frac{x}{5}=\frac{59}{60}\)
\(\frac{x.30+x.20+x.15+x.12}{60}=\frac{59}{60}\)
\(\Leftrightarrow x.30+x.20+x.15+x.12=59\)
\(x.\left(30+20+15+12\right)=59\)
\(x.77=60\)
\(x=\frac{60}{77}\)
x=1
60/77