Question

Решите неравенство......,...

Answer 1

Замена переменной:

$\frac{1}{4x-6y}=t\\\\ \left \{ {{t+x=6} \atop {tx=-27}} \right.$

Значит t  и x корни квадратного уравнения

сумма корней 6; произведение корней -27

z²-6z-27=0

D=36+108=144

z=(6±12)/2

z=(3±6)

Один корень 9; другой корень (-3)

$\left \{ {{x=9} \atop {\frac{1}{4x-6y} =-3}} \right. \left \{ {{x=-3} \atop {\frac{1}{4x-6y} =9}} \right. \\\\\left \{ {{x=9} \atop {4x-6y =-\frac{1}{3}}} \right. \left \{ {{x=-3} \atop {4x-6y =\frac{1}{9}}} \right.$

$\left \{ {{x=9} \atop {-6y =-\frac{1}{3}-36}} \right. \left \{ {{x=-3} \atop {-6y =\frac{1}{9}+12}} \right. \\\\\left \{ {{x=9} \atop {-6y =-\frac{109}{3}}} \right. \left \{ {{x=-3} \atop {-6y =\frac{109}{9}}} \right. \\\\\left \{ {{x=9} \atop {y =+\frac{109}{18}}} \right. \left \{ {{x=-3} \atop {y =-\frac{109}{54}}} \right.$