Respuesta :
Using a system of equations, it is found that the two consecutive numbers can be 8 and 9, or 3 and 4.
What is a system of equations?
A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the numbers are consecutive, hence they are n(smaller number) and n+1(larger number).
The square root of the bigger number is 5 less than the smaller number, hence:
[tex]\sqrt{n+1} = n - 5[/tex]
[tex](\sqrt{n+1})^2 = (n - 5)^2[/tex]
[tex]n^2 - 10n + 25 = n + 1[/tex]
[tex]n^2 - 11n + 24 = 0[/tex]
[tex](n - 8)(n - 3)[/tex]
The solutions are n = 8 and n = 3. Hence, the consecutive numbers can be 8 and 9, or 3 and 4.
More can be learned about a system of equations at https://brainly.com/question/24342899
