Решить неравенство [latex]\sqrt{x+8}\ \textless \ x+2[/latex]

[latex]\sqrt{x+8}\ \textless \ x+2[/latex] [latex] \left \{ {{x+8 \geq 0} \atop {x+2\ \textgreater \ 0}} \atop {( \sqrt{x+8})^2\ \textless \ (x+2)^2 } \right. [/latex] [latex] \left \{ {{x \geq -8} \atop {x\ \textgreater \ -2}} \atop {x+8\ \textless \ x^2+4x+4 } \right. [/latex] [latex] \left \{ {{x \geq -8} \atop {x\ \textgreater \ -2}} \atop {-x^2-3x+4\ \textless \ 0 } \right. [/latex] [latex]\left \{ {{x \geq -8} \atop {x\ \textgreater \ -2}} \atop {x^2+3x-4\ \textgreater \ 0 } \right.[/latex] [latex]x^2+3x-4=0[/latex] [latex]D=3^2-4*1*(-4)=25[/latex] [latex]x_1= \frac{-3+5}{2} =1[/latex] [latex]x_2= \frac{-3-5}{2} =-4[/latex] [latex]\left \{ {{x \geq -8} \atop {x\ \textgreater \ -2}} \atop {(x-1)(x+4)\ \textgreater \ 0 } \right. [/latex] ----------[-8]-------------------------------------------               ///////////////////////////////////////////// -----------------------(-2)------------------------------                             ///////////////////////////////          +                        -                     + ----------------(-4)------------------(1)--------------- //////////////////                         ////////////////// Ответ: [latex](1;+[/latex] ∞ [latex])[/latex]