2x-5\\O.D.3.:\;x^2-3x+2\geq0\\x^2-3x+2=0\\D=9-4\cdot2=1\\x_1=2,\;x_2=1\\(x-1)(x-2)\geq0\Rightarrow x\in(-\infty;1]\cup[2;\;+\infty))\\x^2-3x+2>(2x-5)^2\\x^2-3x+2>4x^2-20x+25\\-3x^2+17x-23>0\\3x^2-17x+23<0\\3x^2-17x+23=0\\D=289-4\cdot3\cdot23=289-276=13\\x_1=\frac{17+\sqrt{13}}6,\;x_2=\frac{17-\sqrt{13}}6\\c\;O.D.3.:\;x\in(-\infty;\;1]\cup\left[2,\;\frac{17+\sqrt{13}}6\right)" alt="1)\;\sqrt{x^2-3x+2}>2x-5\\O.D.3.:\;x^2-3x+2\geq0\\x^2-3x+2=0\\D=9-4\cdot2=1\\x_1=2,\;x_2=1\\(x-1)(x-2)\geq0\Rightarrow x\in(-\infty;1]\cup[2;\;+\infty))\\x^2-3x+2>(2x-5)^2\\x^2-3x+2>4x^2-20x+25\\-3x^2+17x-23>0\\3x^2-17x+23<0\\3x^2-17x+23=0\\D=289-4\cdot3\cdot23=289-276=13\\x_1=\frac{17+\sqrt{13}}6,\;x_2=\frac{17-\sqrt{13}}6\\c\;O.D.3.:\;x\in(-\infty;\;1]\cup\left[2,\;\frac{17+\sqrt{13}}6\right)" align="absmiddle" class="latex-formula">
8-2x\\O.D.3.:\;-x^2+6x-5\geq0\\x^2-6x+5\leq0\\x^2-6x+5=0\\D=36-4\cdot5=16\\x_1=5,\;x_2=1\\(x-1)(x-5)\leq0\Rightarrow x\in[1;5]\\\sqrt{-x^2+6x-5}>8-2x\\-x^2+6x-5>(8-2x)^2\\-x^2+6x-5>64-32x+4x^2\\-5x^2+38x-69>0\\5x^2-38x+69<0\\5x^2-38x+69=0\\D=1444-4\cdot5\cdot69=64\\x_1=3,\;x_2=4,6\\5(x-3)(x-4,6)<0\Rightarrow x\in(3;\;4,6)\\c\;O.D.3.:\;x\in(3;\;4,6)" alt="2)\;\sqrt{-x^2+6x-5}>8-2x\\O.D.3.:\;-x^2+6x-5\geq0\\x^2-6x+5\leq0\\x^2-6x+5=0\\D=36-4\cdot5=16\\x_1=5,\;x_2=1\\(x-1)(x-5)\leq0\Rightarrow x\in[1;5]\\\sqrt{-x^2+6x-5}>8-2x\\-x^2+6x-5>(8-2x)^2\\-x^2+6x-5>64-32x+4x^2\\-5x^2+38x-69>0\\5x^2-38x+69<0\\5x^2-38x+69=0\\D=1444-4\cdot5\cdot69=64\\x_1=3,\;x_2=4,6\\5(x-3)(x-4,6)<0\Rightarrow x\in(3;\;4,6)\\c\;O.D.3.:\;x\in(3;\;4,6)" align="absmiddle" class="latex-formula">
x(2+\sqrt{12-2x-x^2})\\O.D.3.:\;12-2x-x^2\geq0\\x^2+2x-12\leq0\\x^2+2x-12=0\\D=4+4\cdot12=52=(2\sqrt{13})^2\\x_1=-1-\sqrt{13},\;x_2=-1+\sqrt{13}\\(x+1+\sqrt{13})(x+1-\sqrt{13})\leq0\Rightarrow x\in[-1-\sqrt{13};\;-1+\sqrt{13}]" alt="3)\;x^2>x(2+\sqrt{12-2x-x^2})\\O.D.3.:\;12-2x-x^2\geq0\\x^2+2x-12\leq0\\x^2+2x-12=0\\D=4+4\cdot12=52=(2\sqrt{13})^2\\x_1=-1-\sqrt{13},\;x_2=-1+\sqrt{13}\\(x+1+\sqrt{13})(x+1-\sqrt{13})\leq0\Rightarrow x\in[-1-\sqrt{13};\;-1+\sqrt{13}]" align="absmiddle" class="latex-formula">
2x+x\sqrt{12-2x-x^2}\\(x^2-2x)^2>x^2(12-2x-x^2)\\x^4-4x^3+4x^2>12x^2-2x^3-x^4\\2x^4-2x^3-8x^2>0\\2x^2(x^2-x-4)>0\\x^2\left(x-\frac{1-\sqrt{17}}2\right)\left(x-\frac{1+\sqrt{17}}2\right)\Rightarrow x\in(-\infty;0)\cup\left(\frac{1+\sqrt{17}}2;\;+\infty\right)" alt="\\x^2>2x+x\sqrt{12-2x-x^2}\\(x^2-2x)^2>x^2(12-2x-x^2)\\x^4-4x^3+4x^2>12x^2-2x^3-x^4\\2x^4-2x^3-8x^2>0\\2x^2(x^2-x-4)>0\\x^2\left(x-\frac{1-\sqrt{17}}2\right)\left(x-\frac{1+\sqrt{17}}2\right)\Rightarrow x\in(-\infty;0)\cup\left(\frac{1+\sqrt{17}}2;\;+\infty\right)" align="absmiddle" class="latex-formula">
![c\;O.D.3.:\;x\in[-1-\sqrt{13};\;0)\cup\left(\frac{1+\sqrt{17}}2;-1+\sqrt{13}\right]](https://tex.z-dn.net/?f=c%5C%3BO.D.3.%3A%5C%3Bx%5Cin%5B-1-%5Csqrt%7B13%7D%3B%5C%3B0%29%5Ccup%5Cleft%28%5Cfrac%7B1%2B%5Csqrt%7B17%7D%7D2%3B-1%2B%5Csqrt%7B13%7D%5Cright%5D "c\;O.D.3.:\;x\in[-1-\sqrt{13};\;0)\cup\left(\frac{1+\sqrt{17}}2;-1+\sqrt{13}\right]")