[latex] \sqrt{2x+15} - \sqrt{2x-1} = \frac{10}{ \sqrt{2x-1} } [/latex]

[latex] \sqrt{2x+15} - \sqrt{2x-1} = \frac{10}{ \sqrt{2x-1} } [/latex] ОДЗ: [latex] \left \{ {{2x+15 \geq 0} \atop {2x-1\ \textgreater \ 0}} \right. [/latex] [latex] \left \{ {{2x \geq -15} \atop {2x\ \textgreater \ 1}} \right. [/latex] [latex] \left \{ {{x \geq -7.5} \atop {x\ \textgreater \ 0.5}} \right. [/latex] [latex]x[/latex] ∈ [latex](0.5;+[/latex] ∞ [latex])[/latex] [latex]\sqrt{2x+15}* \sqrt{2x-1} - (\sqrt{2x-1})^2 = 10[/latex] [latex]\sqrt{(2x+15)(2x-1)}- (2x-1}) = 10[/latex] [latex]\sqrt{4x^2+28x-15} = 10+2x-1[/latex] [latex]\sqrt{4x^2+28x-15} =2x+9[/latex] [latex] \left \{ {{2x+9 \geq 0} \atop {(\sqrt{4x^2+28x-15})^2 =(2x+9)^2}} \right. [/latex] [latex] \left \{ {{2x \geq 9} \atop {4x^2+28x-15} =4x^2+36x+81} \right. [/latex] [latex]\left \{ {{x \geq -4.5} \atop {8x=-96} \right. [/latex] [latex]\left \{ {{x \geq -4.5} \atop {x=-12} \right. [/latex] Ответ: нет корней