Question

$\sqrt{x+16}-x+4=0$

Answer 1

Ответ:

$9$

Пошаговое объяснение:

$\sqrt{x+16}-x+4=0\\ \\ \sqrt{x+16}=x-4 \\ \\ \left \{ {{x-4\geq 0} \atop {x+16=(x-4)^2}} \right. \\ \\ \left \{ {{x\geq 4} \atop {x+16=x^2-2\cdot x \cdot4+4^2}} \right. \\ \\ \left \{ {{x\geq 4} \atop {x+16=x^2-8x+16}} \right. \\ \\ \left \{ {{x\geq 4} \atop {x^2-8x+16-x-16=0}} \right. \\ \\ \left \{ {{x\geq 4} \atop {x^2-9x=0}} \right. \\ \\ \left \{ {{x\geq 4} \atop {x(x-9)=0}} \right. \\ \\ \left \{ {{x\geq 4} \atop \left[\begin{array}{c}{x=0}&{x-9=0}\\ \end{array}}} \right.$

$\\ \\ \left \{ {{x\geq 4} \atop \left[\begin{array}{c}{x=0}&{x=9}\\ \end{array}}} \right.$

$x=9$