Sqrt(2*x+6)+sqrt(x-1)=6

[latex] \sqrt{2x+6} +\sqrt{x-1} =6[/latex] ОДЗ: [latex] \left \{ {{2x+6 \geq 0} \atop {x-1 \geq 0}} \right. [/latex] [latex] \left \{ {{x \geq -3} \atop {x \geq 1}} \right. [/latex] [latex]x[/latex]∈[latex][1;+[/latex]∞[latex])[/latex] [latex](\sqrt{2x+6} +\sqrt{x-1} )^2=6^2[/latex] [latex]2x+6+x-1+2 \sqrt{(2x+6)(x-1)}=36 [/latex] [latex]2 \sqrt{(2x+6)(x-1)}=31-3x[/latex] [latex]31-3x \geq 0[/latex] [latex]-3x \geq -31[/latex] [latex]x \leq 10 \frac{1}{3} [/latex] [latex]4(2x+6)(x-1)=(31-3x)^2[/latex] [latex]8 x^{2} +16x-24=961+9 x^{2} -186x[/latex] [latex] x^{2} -202x+985=0[/latex] [latex]D_1=( \frac{b}{2} )^2-ac=10201-985=9216=96^2[/latex] [latex]x_1=5[/latex] [latex]x_2=197[/latex] не подходит Ответ: 5