Question

2x+1/x+4x/2x+1=5 решите уравнение

Answer 1

$\dfrac{2x+1}{x} +\dfrac{4x}{2x+1} =5\\\\\\\dfrac{2x+1}{x}=a \ \Rightarrow \ \dfrac{x}{2x+1} =\dfrac{1}{a}\\\\\\a+\dfrac{4}{a} =5\\\\\\a^{2}-5a+4=0 \ ; \ a\neq0\\\\Teorema \ Vieta:\\\\a_{1} =1 \ ; \ a_{2} =4\\\\\\1) \ a=1\\\\\\\dfrac{2x+1}{x}=1\\\\2x+1=x\\\\2x-x=-1\\\\x_{1} =-1$

$2) \ a=4\\\\\\\dfrac{2x+1}{x}=4\\\\2x+1=4x\\\\4x-2x=1\\\\2x=1\\\\x_{2} =0,5\\\\Otvet:\boxed{-1 \ ; \ 0,5}$