If \(x=3-3^{1/3}-3^{2/3}\), then what is \(x(x-3)(x-6)\) equal to?
-12
Let \(t=3^{1/3}\), so \(t^3=3\) and \(x=3-t-t^2\). Using \(t^3=3\) and \(t^4=3t\), expansion gives \(x^2=15-3t-5t^2\) and \(x^3=69-9t-27t^2\). Then \(x(x-3)(x-6)=x^3-9x^2+18x=(69-9t-27t^2)-9(15-3t-5t^2)+18(3-t-t^2)=-12\), since all terms in \(t\) and \(t^2\) cancel out.
What is the simplified value of \(\dfrac{(0.25)^3 + (0.05)^3}{(0.5)^3 + (0.1)^3}\)?
What is the simplified value of \(\dfrac{(0.05)^3 + (0.005)^3}{(0.25)^3 + (0.025)^3}\)?
A gardener organizes plants into rows to create a square formation but discovers that 15 plants are not included. If the total number of plants is 3984, then what is the number of plants in each row?