Question

Find x, y and zx³+y³+z³=kfor each k 1 to 100

Answer 1

Since this equation has three variables, there is an infinite number of solutions.

For example, we can define y and z equal to 0, then we calculate the value of x:

`\begin{gathered} k=1,y=0,z=0\colon \\ x^3=1\to x=1 \\ \\ k=2,y=0,z=0\colon \\ x^3=2\to x=\sqrt[3]{2} \end{gathered}`

So, for any value of k, a valid solution is:

`(\sqrt[3]{k},0,0)`