Решить уравнение: 2V(x-1) - V(x+2) =V(5x-10)

[latex] 2\sqrt{x-1} - \sqrt{x+2} = \sqrt{5x-10} \\ 2\sqrt{x-1} = \sqrt{x+2} + \sqrt{5x-10} \\ (2\sqrt{x-1})^{2} = (\sqrt{x+2} + \sqrt{5x-10})^{2} \\ 4(x-1)=x+2+2 \sqrt{(x+2)(5x-10)} +5x-10 \\ 4x-4=6x-8+2 \sqrt{5x^{2}-20} \\ 4x-6x-4+8=2 \sqrt{5x^{2}-20} \\ -2x+4=2 \sqrt{5x^{2}-20} \\ 2-x= \sqrt{5x^{2}-20} \\ (2-x)^{2}= (\sqrt{5x^{2}-20})^{2} \\ 4-4x+ x^{2} =5 x^{2} -20 \\ 4 x^{2} +4x-24=0 \\ x^{2} +x-6=0 \\ D=25;x_{1}=2;x_{2}=-3[/latex] Проверка х=2 ; 2√1-√4=√0-верно х=-3 2√-4-√-1=√-25 не верно Ответ:2