Ответ(ы) на вопрос:
[latex] \sqrt{x+2} \ \textgreater \ x[/latex]
1 случай:
[latex] \left \{ {{x\ \textless \ 0} \atop {x+2 \geq0 }} \right. [/latex]
[latex] \left \{ {{x\ \textless \ 0} \atop {x \geq-2 }} \right. [/latex]
x∈ [latex][-2;0)[/latex]
2 случай:
[latex] \left \{ {{x \geq 0} \atop {( \sqrt{x+2})^2\ \textgreater \ x^2 }} \right. [/latex]
[latex] \left \{ {{x \geq 0} \atop {x+2\ \textgreater \ x^{2} }} \right. [/latex]
[latex] \left \{ {{x \geq 0} \atop {x+2- x^{2} \ \textgreater \ 0} }} \right. [/latex]
[latex] \left \{ {{x \geq 0} \atop { x^{2} -x-2\ \textless \ 0} }} \right. [/latex]
[latex]D=1+8=9[/latex]
[latex]x_1=2[/latex]
[latex]x_2=-1[/latex]
[latex] \left \{ {{x \geq 0} \atop {(x-2)(x+1)\ \textless \ 0} }} \right. [/latex]
x∈ [latex][0;2)[/latex]
общее решение : x ∈ [latex][-2;2)[/latex]
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