Решите уравнние Корень из 7-х²= корень из -6х

[latex]\sqrt{7-x^2}=\sqrt{-6x}[/latex] [latex] \left \{ {{7-x^2 \geq 0} \atop {-6x \geq 0}} \right. [/latex] [latex] \left \{ {{x^2 \leq 7} \atop {x \leq 0}} \right. [/latex] [latex]\left \{ {{x \in [-\sqrt7;\sqrt7]} \atop {x\in(-\infty;0]}} \right.[/latex] ОДЗ: [latex]x\in[-7;0][/latex] [latex]|7-x^2|=|-6x|[/latex] [latex]\left [ {{7-x^2=-6x} \atop {7-x^2=6x}} \right. [/latex] [latex]\left [ {{x^2-6x-7=0} \atop {x^2+6x-7=0}} \right.[/latex] [latex]\left[ x=\pm1 \atop x=\pm7 \right.[/latex] С ОДЗ: [latex]\left[ x=-1 \atop x=-7 \right.[/latex] Ответ: -1; -7

возведем в квадрат 7-х^2=-6х х^2-6х-7=0 д=36-4×1×(-7)=64 х1=(6-8)/2=-1 х2=(6+8)/2=7