Question

Найдите произведение наибольшего корня на количество коней уравнения 24/(x²-3x+10)-x^2+3x=5​

Answer 1

$\displaystyle\bf\\\frac{24}{x^{2} -3x+10} -x^{2} +3x=5\\\\\\\frac{24}{x^{2} -3x+10} -(x^{2} -3x)-5=0\\\\\\x^{2} -3x=m\\\\\\\frac{24}{m+10} -m-5=0\\\\\\\frac{24-m^{2} -10m-5m-50}{m+10} =0\\\\\\\frac{m^{2} +15m+26}{m+10} =0\\\\\\\left \{ {{m^{2} +15m+26=0} \atop {m+10\neq 0}} \right. \\\\\\m^{2} +15m+26=0 \ \ \ \Rightarrow \ \ \ m\neq -10\\\\\\D=15^{2} -4\cdot26=225-104=121=11^{2} \\\\\\m_{1} =\frac{-15+11}{2} =\frac{-4}{2} =-2$

$\displaystyle\bf\\m_{2} =\frac{-15-11}{2} =\frac{-26}{2} =-13\\\\1)\\\\x^{2} -3x=-2\\\\x^{2} -3x+2=0\\\\Teorema \ Vieta \ :\\\\x_{1} +x_ { 2} =3\\\\x_{1} \cdot x_{2} =2\\\\x_{1} =1 \ \ ; \ \ x_{2} =2\\\\2)\\\\x^{2} -3x=-13\\\\x^{2} -3x+13=0\\\\D=(-3)^{2} -4\cdot 13=9-52=-43 < 0\\\\x\in\oslash$

Всего 2 корня , наибольший корень равен 2 .

2 * 2 = 4

Ответ  :  4