Question

Помогите,срочно! √(2x + 3) + √(4 - x) = √(3x + 7)

Answer 1

$sqrt{2x+3} + sqrt{4-x} = sqrt{3x+7}$

ОДЗ: 

$left { {{2x+3 geq 0} atop {4-x geq 0}} atop {3x+7 geq 0}} right.$

$left { {{x geq -1.5} atop {x leq 4}} atop {x geq -2 frac{1}{3} }} right.$

$x$ ∈ $[-1.5;4]$

$(sqrt{2x+3} + sqrt{4-x} )^2= (sqrt{3x+7} )^2$

$2x+3+4-x+2 sqrt{(2x+3)(4-x}) =3x+7$

$x+7+2 sqrt{(2x+3)(4-x}) =3x+7$

$2 sqrt{(2x+3)(4-x}) =2x$

$sqrt{(2x+3)(4-x}) =x$

$left { {{x geq 0} atop {(2x+3)(4-x) =x^2}} right.$

$8x-2x^2+12-3x =x^2$

$3x^2-5x-12=0$

$D=(5)^2-4*3*(-12)=25+144=169=13^2$

$x_1= frac{5+13}{6}=3$

$x_2= frac{5-13}{6}=- frac{8}{6} =- frac{4}{3} =-1 frac{1}{3}$  ∅

Ответ:  $3$