Question

√2х+5-√х+6=1 
помагите

Answer 1

$sqrt{2x+5}- sqrt{x+6}=1;$
ОДЗ:  $left { {{2x+5 geq 0} atop {x+6 geq 0}} right. Rightarrow left { {{xgeq-2,5} atop {x geq-6}} right. Rightarrow xgeq-2,5$
$(sqrt{2x+5}- sqrt{x+6})^2=1^2;$
$2x+5-2sqrt{2x+5} sqrt{x+6}+x+6=1;$
$2sqrt{2x+5}sqrt{x+6}=3x+10;$
$(2sqrt{(2x+5)(x+6)})^2=(3x+10)^2;$
$4(2x+5)(x+6) =9 x^{2}+ 60x+100;$
$8x^{2}+68x+120- 9 x^{2}- 60x-100=0;$
$- x^{2}+8x+20=0;x^{2}-8x-20=0;$
$D_1=16+20=36;x_1=-2;x_2=10;$
Ответ:  $x=-2;x=10;$