We have two positive numbers x and y.
We know that x is 4 less than y, so we can write:

We know that the sum of the square of the two numbers is 62, so we can write:

If we replace x with y we can find the value of y as:

We have to calculate the roots of y:
![\begin{gathered} y=\frac{-(-4)\pm\sqrt[]{(-4)^2-4\cdot1\cdot(-23)}}{2\cdot1} \\ y=\frac{4\pm\sqrt[]{16+92}}{2} \\ y=\frac{4\pm\sqrt[]{108}}{2} \\ y\approx(4\pm10.4)/(2) \\ y_1\approx(4-10.4)/(2)=-3.2\longrightarrow\text{Not valid (it has to be positive)} \\ y_2\approx(4+10.4)/(2)=(14.4)/(2)=7.2 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/poavaime78jueroe22ntdd5cx6a4casqtt.png)
The value of y is 7.2.
Then, the value of x is 7.2 - 4 = 3.2.
We can check the squares as:

The difference between 62.08 and 62 is an error of approximation when rounding the square root of 108.
Answer: the numbers are approximately 3.2 and 7.2.