Question

Розв'яжіть рівняння
$\frac{3x^{2} -9x}{2} -\frac{12}{x^{2} -3x} =3$

Answer 1

$\displaystyle\bf\\\frac{3x^{2} -9x}{2} -\frac{12}{x^{2} -3x} =3\\\\\\\frac{3(x^{2} -3x)}{2} -\frac{12}{x^{2} -3x} =3\\\\\\x^{2} -3x=m \ \ ; \ \ m\neq 0\\\\\\\frac{3m}{2} -\frac{12}{m} -3=0\\\\\\\frac{3m^{2} -6m-24}{2m} =0\\\\\\3m^{2} -6m-24=0 \ |:3\\\\\\m^{2} -2m-8=0\\\\\\Teorema \ Vieta:\\\\\\m_{1} + m_{2} =2\\\\\\m_{1} \cdot m_{2} =-8\\\\\\m_{1} =4 \ \ ; \ \ m_{2} =-2$

$\displaystyle\bf\\1)\\\\x^{2} -3x=4\\\\\\x^{2} -3x-4=0\\\\\\Teorema \ Vieta:\\\\\\\boxed{x_{1} =-1 \ \ ; \ \ x_{2} =4}\\\\\\2)\\\\x^{2} -3x=-2\\\\\\x^{2}-3x+2=0\\\\\\Teorema \ Vieta:\\\\\\x_{3} =1 \ \ ; \ \ x_{4} =2\\\\\\Otvet: \ -1 \ ; \ 4 \ ; \ 1 \ ; \ 2$