Question

Решить уравнение на фотографии. 11 класс

Answer 1

ОДЗ: 
$left { {{2x+3 geq 0} atop {2x+5 textgreater 0}} right. textless = textgreater left { {{x geq -1.5} atop {x textgreater -2.5}} right. textless = textgreater x geq -1.5$

Решение:

$sqrt{2x+3} +sqrt{2x+5} = frac{4}{sqrt{2x+5} } |*sqrt{2x+5} \ \ sqrt{2x+3} *sqrt{2x+5} +2x+5=4 \ sqrt{(2x+3)(2x+5)} =-1-2x \ sqrt{4x^2+10x+6x+15}=-(2x+1) \ sqrt{4x^2+16x+15}=-(2x+1) \ \ left { {{-(2x+1) geq 0} atop {4x^2+16x+15=4x^2+4x+1}} right. textless = textgreater left { {{2x+1 leq 0} atop {12x=-14}} right. textless = textgreater left { {{x leq -0.5} atop {x=- frac{7}{6} }} right. textless = textgreater x=- frac{7}{6} \ \ OTBET: - frac{7}{6}$