c)
[tex](x^{2}-5x)(x^{2}-5x+2) = 24\\\\(x^{2}-5x)(x^}2-5x+2)-24 = 0\\\\Niech \ \ t = x^{2}-5x\\\\t(t+2)-24 = 0\\\\t^{2}-2t-24 = 0\\\\\Delta = (-2)^{2}-4\cdot(-24) = 4 + 96 = 100\\\\\sqrt{\Delta} = \sqrt{100} = 10\\\\t_1 = \frac{-2-10}{2} = \frac{-12}{2} = -6 \ \ \vee \ \ t_2 = \frac{-2+10}{2} = \frac{8}{2} = 4\\\\\\x^{2}-5x = -6\\\\x^{2}-5x+6 = 0\\\\\Delta_{x} = (-5)^{2}-4\cdot6 = 25-24 = 1\\\\\sqrt{\Delta _{x}} = 1\\\\x_1 = \frac{5-1}{2}=\frac{4}{2} = 2\\\\x_2 = \frac{5+1}{2} = \frac{6}{2} = 3[/tex]
[tex]x^{2}-5x=4\\\\x^{2}-5x-4 = 0\\\\\Delta _{x} = (-5)^{2}-4\cdot(-4) = 25 + 16 = 41\\\\\sqrt{\Delta_{x}} = \sqrt{41}\\\\x_3 = \frac{5-\sqrt{41}}{2} \\\\x_4 = \frac{5+\sqrt{41}}{2}\\\\x \in \{\frac{5-\sqrt{41}}{2}, 2,3,\frac{5+\sqrt{41}}{2}\}[/tex]
