[tex]\displaystyle\bf\\\Big(\frac{x^{2} -6}{x} \Big)^{2} -5=4\Big(\frac{x^{2} -6}{x} \Big)\\\\\\\frac{x^{2}-6 }{x} =m\\\\\\m^{2} -4m-5=0\\\\D=(-4)^{2} -4\cdot(-5)=16+20=36=6^{2} \\\\\\m_{1}=\frac{4-6}{2} =-1\\\\\\m_{2} =\frac{4+6}{2} =5\\\\\\1) \ m=-1\\\\\\\frac{x^{2} -6}{x} =-1\\\\\\x^{2} -6=-x \ \ , \ \ x\neq 0\\\\x^{2} +x-6=0\\\\D=1^{2} -4\cdot(-6)=1+24=25=5^{2} \\\\\\x_{1} =\frac{-1-5}{2} =-3\\\\\\x_{2} =\frac{-1+5}{2} =2[/tex]

[tex]\displaystyle\bf\\2) \ m=5\\\\\\\frac{x^{2} -6}{x} =5\\\\\\x^{2} -6=5x \ \ , \ \ x\neq 0\\\\x^{2} -5x-6=0\\\\D=(-5)^{2} -4\cdot(-6)=25+24=49=7^{2} \\\\\\x_{3} =\frac{5-7}{2} =-1\\\\\\x_{4} =\frac{5+7}{2} =6\\\\\\Otvet \ : \ -3 \ ; \ 2 \ ; \ -1 \ ; \ 6[/tex]

[tex]\displaystyle\bigg(\frac{x^2-6}{x}\bigg)^2-5=4\bigg(\frac{x^2-6}{x}\bigg)\\\\\bigg(\frac{x^2-6}{x}\bigg)^2-4\bigg(\frac{x^2-6}{x}\bigg)-5=0[/tex]

Пусть [tex]\displaystyle\frac{x^2-6}{x}=t[/tex], тогда

[tex]t^2-4t-5=0\\D=(-4)^2-4\times(-5)=16+20=36=6^2\\\\t_{1,2}=\dfrac{4\pm6}{2}=\bigg[^5_{-1}[/tex]

Возвращаем переменную и решаем 2 уравнения

[tex]\displaystyle\\\frac{x^2-6}{x}=5\\ \\\frac{x^2-5x-6}{x} =0\\\text{OD3}:x\neq0= > \\x^2-5x-6=0\\x_1=-1,x_2=6[/tex]

[tex]\displaystyle\\\frac{x^2-6}{x}=-1\\ \\\frac{x^2+x-6}{x} =0\\\text{OD3}:x\neq0= > \\x^2+x-6=0\\x_3=-3,x_4=2[/tex]