# Question #a2758

Jan 29, 2018

The two numbers are $2$ and $3$.

#### Explanation:

The easiest way to go about this question is to simply try all the combinations and see what we get.

We have two (unordered) pairs which could possibly work: $\left(1 , 4\right)$ and $\left(2 , 3\right)$.

Now we need to check which of these satisfies the second condition.

${1}^{3} + 2 \left({4}^{2}\right) = 33$

${2}^{3} + 2 \left({3}^{2}\right) = 26$

We see that $26$ is the smallest number so our pair is $\left(2 , 3\right)$.