Имеет 1 единственный корень 
x(x^2+2)=4<=>x^2=\frac{4}{x}+2 <=> x(x-2)(x+2)+2(x-2)=0<=>(x-2)(x^2+2x+2)=0;\left \{ {{x-2=0} \atop {x^2+2x+2=0}} \right. <=>\left \{ {{x=2} \atop {x=2}} \right." alt="\frac{1}{2}x^{2} =2-x <=> x(x^2+2)=4<=>x^2=\frac{4}{x}+2 <=> x(x-2)(x+2)+2(x-2)=0<=>(x-2)(x^2+2x+2)=0;\left \{ {{x-2=0} \atop {x^2+2x+2=0}} \right. <=>\left \{ {{x=2} \atop {x=2}} \right." align="absmiddle" class="latex-formula"> т.к