Question

Решите уравнение: х2+4х=4+2|х+2| модуль- ||

Answer 1

$x^{2} +4x=4+2|x+2| \\ \left \{ {{x+2 \geq 0} \atop {x^2+4x=4+2(x+2)}} \right. \\ \left \{ {{{x \geq -2} \atop {x^2+4x=4+2x+4}} \right. \\ \left \{ {{x \geq -2} \atop {x^2+2x-8=0}} \right. \\ x^2+2x-8=0 \\ D=4+32=6^2 \\ x12= \frac{-2+-6}{2} \\ x=2 \\ x=-4 \\ \\ \left \{ {{x \geq -2} \atop {x=2, x=-4}} \right. \\ x=2 \\ \\ \left \{ {{x \ \textless \ -2} \atop {x^2+4x=4+2(-x-2)}} \right. \\ \left \{ {x \ \textless \ -2} \atop {x^2+4x=4-2x-4}} \right. \\ \left \{ {{x \ \textless \ -2} \atop {x^2+4x-4+2x+4=0}} \right.$

$\left \{ {{x \ \textless \ -2} \atop {x^2+4x-4+2x+4=0}} \right. \\ \left \{ {{x \ \textless \ -2} \atop {x^2+6x=0}} \right. \\ x(x+6)=0 \\ x=0 \\ x=-6 \\ \left \{ {{x \ \textless \ -2} \atop {x=0, x=-6}} \right. \\ x=-6$
ответ: x=2 или х=-6