Theo bài ra , ta có :
\(\frac{144}{x+2}-\frac{100}{x}=2\left(ĐKXĐ:x\ne0;x\ne2\right)\)
Quy đồng cà khử mẫu ta được :
\(144x-100\left(x+2\right)=2x\left(x+2\right)\)
\(\Leftrightarrow144x-100x-200=2x^2+4x\)
\(\Leftrightarrow44x-200-2x^2-4x=0\)
\(\Leftrightarrow-2x^2+40x-200=0\)
\(\Leftrightarrow-2\left(x^2-20x+100\right)=0\)
\(\Leftrightarrow x^2-20x+100=0\)
\(\Leftrightarrow\left(x-10\right)^2=0\)
\(\Leftrightarrow x-10=0\)
\(\Leftrightarrow x=10\)
Vậy \(S=\left\{10\right\}\)
Chúc bạn hok tốt =))
\(\frac{144}{x+2}-\frac{100}{x}=2\left(1\right)\)
ĐKXĐ : \(x\ne-2;x\ne0\)
MTC : x(x + 2 )
\(\left(1\right)\Leftrightarrow\frac{144x}{x\left(x+2\right)}-\frac{100\left(x+2\right)}{x\left(x+2\right)}=\frac{2x\left(x+2\right)}{x\left(x+2\right)}\)
\(\Leftrightarrow144x-100x-200=2x^x+4x\)
\(\Leftrightarrow2x^2+4x-144x+100x+200=0\)
\(\Leftrightarrow2x^2-40x+200=0\)\(\Leftrightarrow2\left(x^2-20x+10^2\right)=0\)
\(\Leftrightarrow2\left(x-10\right)^2=0\)\(\Leftrightarrow\left(x-10\right)^2=0\)
\(\Leftrightarrow x-10=0\Leftrightarrow x=10\left(chọn\right)\)
Vậy tập nghiệm của phương trình là S = { 10 }
\(\dfrac{144}{x+2}\)\(-\)\(\dfrac{100}{x}\)=2
\(\Leftrightarrow\)\(\dfrac{144x}{\left(x+2\right)x}-\dfrac{100\left(x+2\right)}{x\left(x+2\right)}=\dfrac{2x\left(x+2\right)}{x\left(x+2\right)}\)
\(\Leftrightarrow144x-100\left(x+2\right)=2x\left(x+2\right)\)
\(\Leftrightarrow144x-100x-200=2x^2+4x\)
\(\Leftrightarrow-2x^2+144x-100x-4x=200\)
\(\Leftrightarrow-2x^2+40x=200\)
\(\Leftrightarrow-2x^2+40x-200=0\)
\(\Leftrightarrow-2\left(x^2-20x+100\right)=0\)
\(\Leftrightarrow x^2-20x+100=0\)
\(\Leftrightarrow\left(x-10\right)^2=0\)
\(\Leftrightarrow x-10=0\)
\(\Leftrightarrow x=10\)
mình làm từng bước mong bạn sẽ hiểu !!!
CHÚC BẠN HC TỐT NHA !!!
