X³/2 +2/x³=1 find x³.x³.x³ plz solve this algebra question..i get 8 ans

Let x^3/2=y than equation becomes y + 1/y=1 or y^2 + 1 = y since x^3/2=y therefore x^3=2y so we get x^3.x^3.x^3=8y^3 or x^3.x^3.x^3=8(y^2+1)^3 (since y=y^2+1)As y^2+1 is always positive so its minimum value will be on y=0 that is 1so x^3.x^3.x^3= 8(0^2+1)^3= 8