_________ /5+2х-х^2=х+1

[latex] sqrt{5+2x- x^{2} } = x-1 \ (sqrt{5+2x- x^{2} })^{2} = (x-1)^{2} \ 5+2x- x^{2} = x^{2} - 2x + 1 \ 2x^{2} - 4x - 4 = 0 \ x^{2} - 2x - 2 = 0 \ D = 4 + 8 = 12 \ sqrt{D} = 2 sqrt{3} \ x_{1} = frac{2+ 2 sqrt{3}}{2} = 1 + sqrt{3}} \ x_{2} = frac{2- 2 sqrt{3}}{2} = 1 - sqrt{3}} \[/latex]Проверка корней:[latex]x=1+ sqrt{3}} \ sqrt{5+2(1+ sqrt{3} )- (1+ sqrt{3}} )^{2} }} = (1+ sqrt{3}} )-1 \ sqrt{5+2+ 2sqrt{3}- 1- 2sqrt{3}-3} }} = sqrt{3}}\ sqrt{3}} = sqrt{3}}\ [/latex] (ВЕРНО)[latex]x=1- sqrt{3}} \ sqrt{5+2(1- sqrt{3} )- (1- sqrt{3}} )^{2} }} = (1- sqrt{3}} )-1 \ sqrt{5+2- 2sqrt{3}- 1+ 2sqrt{3}-3} }} = -sqrt{3}}\ sqrt{3}} = - sqrt{3}}\ [/latex](НЕВЕРНО)Ответ:  1+√3.