Решите иррациональное уравнение. [latex]\sqrt{5+\sqrt[3]x}+\sqrt{5-\sqrt[3]x}=\sqrt[3]{x}.[/latex]

[latex]\sqrt{5+\sqrt[3]{x}}+\sqrt{5-\sqrt[3]{x}}=\sqrt[3]{x}\\\\t=\sqrt[3]{x}\; ,\; \; \; \sqrt{5+t}+\sqrt{5-t}=t\; ,\; \; t \geq 0\\\\ODZ:\; \; \left \{ {{5+t \geq 0} \atop {5-t \geq 0}} \right. \; \left \{ {{t \geq -5} \atop {t \leq 5}} \right. \to \; \; -5 \leq t \leq 5\\\\\underline {0 \leq t \leq 5}\\\\(5+t)+2\sqrt{25-t^2}+(5-t)=t^2\\\\2\sqrt{25-t^2}=t^2-10\\\\4(25-t^2)=t^4-20t^2+100\\\\t^4-16t^2=0\\\\t^2(t^2-16)=0[/latex] [latex]t^2(t-4)(t+4)=0\\\\t_1=0,\; t=4\; ,\; t=-4\notin ODZ\\\\\sqrt[3]{x}=0\; ,\; \; x=0\\\\\sqrt[3]{x}=4\; ,\; \ x=4^3=48[/latex]