1)
[tex]\it (\sqrt3+\sqrt7)^2=10+2\sqrt{21}=10+\sqrt{84}\\ \\ 9=\sqrt{81}<\sqrt{84}<\sqrt{100}=10 \Rightarrow 9<\sqrt{84}<10|_{+10} \Rightarrow \\ \\ \Rightarrow19<10+\sqrt{84}<20 \Rightarrow [10+\sqrt{84}]=9 \Rightarrow [(\sqrt3+\sqrt7)^2]=19[/tex]
[tex]\it 2)\ \dfrac{2x-1}{1-x}\geq \dfrac{3x+2}{1-2x} |_{\cdot{(-1)}} \Rightarrow \dfrac{2x-1}{x-1}\leq \dfrac{3x+2}{2x-1} \Rightarrow\\ \\ \\ \Rightarrow \dfrac{2x-1}{x-1}- \dfrac{3x+2}{2x-1}\leq0 \Rightarrow \dfrac{(2x-1)(2x-1)-(x-1)(3x+2)}{(x-1)(2x-1)}\leq0\Rightarrow\\ \\ \\ \Rightarrow \dfrac{4x^2-4x+1-3x^2-2x+3x+2}{2x^2-3x+1}\leq0 \Rightarrow \dfrac{x^2-3x+3}{2x^2-3x+1}\leq0\ \ \ \ \ (*)[/tex]
[tex]\it x^2-3x+3 = \Big(x-\dfrac{3}{2}\Big)^2+\dfrac{3}{4}>0 \stackrel{(*)}{\Longrightarrow} 2x^2-3x+1<0 \Rightarrow\\ \\ \\ \Rightarrow 2x^2-x-2x+1<0 \Rightarrow x(2x-1)-(2x-1)<0 \Rightarrow\\ \\ \Rightarrow (2x-1)(x-1)<0 \Rightarrow x\in\Big(\dfrac{1}{2},\ 1\Big)[/tex]
