|5X-3|<4
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\(\dfrac{3}{{5x - 1}} + \dfrac{2}{{3 - 5x}} = \dfrac{4}{{\left( {1 - 5x} \right)\left( {x - 3} \right)}}\)
ĐKXĐ: \(x \ne \dfrac{1}{5};x\ne \dfrac{3}{5};x \ne 3\)
\( \Leftrightarrow 3\left( {3 - 5x} \right)\left( {x - 3} \right) + 2\left( {5x - 1} \right)\left( {x - 3} \right) + 4\left( {3 - 5x} \right) = 0\\ \Leftrightarrow 9x - 27 - 15{x^2} + 45x + 10{x^2} - 30x - 2x + 6 + 12 - 20x = 0\\ \Leftrightarrow - 5{x^2} + 2x - 9 = 0 \)
\(\Rightarrow\) Phương trình vô nghiệm.
\(5^x+5^{x+1}+5^{x+2}+5^{x+3}=1+2+3+...+87+88-4^2\)
=>\(5^x+5^x\cdot5+5^x\cdot25+5^x\cdot125=88\cdot\dfrac{\left(88+1\right)}{2}-16\)
=>\(156\cdot5^x=44\cdot89-16=3900\)
=>\(5^x=\dfrac{3900}{156}=25\)
=>x=2
Lời giải:
$5^x+5^{x+1}+5^{x+2}+5^{x+3}=1+2+3+...+87+88-4^2$
$5^x(1+5+5^2+5^3)=88.89:2-16$
$5^x.156=3900$
$5^x=3900:156=25=5^2$
$\Rightarrow x=2$
Hình như bạn ghi sai đề. Đề đúng: \(\left(5x+1\right)^2-\left(5x-3\right)\left(5x+3\right)=30\)
\(\left(5x+1\right)^2-\left(5x-3\right)\left(5x+3\right)=30\)
\(\Leftrightarrow25x^2+10x+1-25x^2+9=30\)
\(\Leftrightarrow10x+10=30\)
\(\Leftrightarrow10x=20\)
\(\Leftrightarrow x=2\)
\(\frac{3}{\left(5x-1\right)}+\frac{2}{3-5x}=\frac{4}{\left(5x-1\right)\left(3-5x\right)}\)
\(\Rightarrow9-15x+10x-2=4\)
\(\Leftrightarrow3-5x=0\)
\(\Leftrightarrow x=\frac{3}{5}\)
\(\frac{3}{\left(5x-1\right)}+\frac{2}{3-5x}=\frac{4}{\left(5x-1\right)\left(3-5x\right)}\)
⇒9 − 15x + 10x − 2 = 4
⇔3 − 5x = 0
⇔x =\(\frac{3}{5}\)
\(ĐKXĐ:x\ne\frac{1}{5},x\ne\frac{3}{5}\)
Ta có : \(\frac{3}{5x-1}=\frac{2}{3-5x}=\frac{4}{\left(1-5x\right)\left(5x-3\right)}\)
\(\Leftrightarrow\frac{3\left(3-5x\right)}{\left(5x-1\right)\left(3-5x\right)}-\frac{2\left(5x-1\right)}{\left(5x-1\right)\left(3-5x\right)}+\frac{4}{\left(5x-1\right)\left(5x-3\right)}=0\)
\(\Rightarrow9-15x-10x+2+4=0\)
\(\Leftrightarrow-25x=-15\)
\(\Leftrightarrow x=\frac{3}{5}\) ( không thỏa mãn \(ĐKXĐ\) )
Vậy pt đã cho vô nghiệm
=>5x-3<4 hoac 5x-3<-4
5x-3<4
5x<7
x<7/5
5x-3<-4
5x<-1
x<-1/5