[latex]( \frac{1}{ x^{2}-7x+12 } + \frac{x-4}{3-x} ) [/latex] × [latex] \sqrt{6x-x^{2} } \leq 0[/latex]

ОДЗ x²-7x+12=0 (x-3)(x-4)=0 x₁=3 x₂=4 3-x=0 x=3 6x-x²≥0 x(6-x)≥0 x(x-6)≤0 x∈[0;6] [latex]( \frac{1}{(x-3)(x-4)} - \frac{x-4}{x-3}) \sqrt{x(6-x)} \leq 0[/latex] [latex] \frac{1-(x-4)(x-4)}{(x-3)(x-4)} * \sqrt{x(6-x)} \leq 0[/latex] [latex] \frac{1- x^{2}+8x-16 }{(x-3)(x-4)} * \sqrt{x(6-x)} \leq 0[/latex] [latex] \frac{- (x^{2}-8x+15) }{(x-3)(x-4)} * \sqrt{x(6-x)} \leq 0[/latex] [latex] \frac{ (x^{2}-8x+15) }{(x-3)(x-4)} * \sqrt{x(6-x)} \geq 0 [/latex] D=8*8-4*15=4 x₁=(8-2)/2=3 x₂=(8+2)/2=5 [latex] \frac{ (x-3)(x-5)) }{(x-3)(x-4)} * \sqrt{x(6-x)} \geq 0[/latex] [latex] \frac{x-5}{x-4}* \sqrt{x(6-x)} \geq 0 [/latex] x∈[5; +∞) учитывая ОДЗ х∈[5; 6]