Question

Решить уравнение $\sqrt{x^{3}+x^{2}+x}=x\sqrt{x}$

Answer 1

$\sqrt{x^{3} + x^{2} + x} = x\sqrt{x}$

$\displaystyle \left \{ {{x\sqrt{x} \geq 0~~~~~~~~~~~~~~~~~~~~~~~} \atop {(\sqrt{x^{3} + x^{2} + x})^{2} = (x\sqrt{x}})^{2}} \right.$

$\displaystyle \left \{ {{x \geq 0~~~~~~~~~~~~~~~} \atop {x^{3} + x^{2} + x = x^{3}}} \right.$

$\displaystyle \left \{ {{x \geq 0~~~~~~~} \atop {x^{2} + x = 0}} \right.$

$\displaystyle \left \{ {{x \geq 0~~~~~~~~~} \atop {x(x+1) = 0}} \right.$

$\displaystyle \left \{ {{x \geq 0~~~} \atop {\displaystyle \left [ {{x=0~~} \atop {x=-1}} \right. }} \right.$

$\displaystyle \left \{ {{x \geq 0} \atop {x = 0}} \right.$

Ответ: 0

Answer 2

Ответ: х=0

Объяснение: