Question

$sqrt{2x+15} - sqrt{2x-1} = frac{10}{ sqrt{2x-1} }$

Answer 1

$sqrt{2x+15} - sqrt{2x-1} = frac{10}{ sqrt{2x-1} }$
ОДЗ:
$left { {{2x+15 geq 0} atop {2x-1 textgreater 0}} right.$
$left { {{2x geq -15} atop {2x textgreater 1}} right.$
$left { {{x geq -7.5} atop {x textgreater 0.5}} right.$
$x$ ∈ $(0.5;+$ ∞ $)$

$sqrt{2x+15}* sqrt{2x-1} - (sqrt{2x-1})^2 = 10$
$sqrt{(2x+15)(2x-1)}- (2x-1}) = 10$
$sqrt{4x^2+28x-15} = 10+2x-1$
$sqrt{4x^2+28x-15} =2x+9$
$left { {{2x+9 geq 0} atop {(sqrt{4x^2+28x-15})^2 =(2x+9)^2}} right.$
$left { {{2x geq 9} atop {4x^2+28x-15} =4x^2+36x+81} right.$
$left { {{x geq -4.5} atop {8x=-96} right.$
$left { {{x geq -4.5} atop {x=-12} right.$
Ответ: нет корней