Answer:
19 and 12
Step-by-step explanation:
Let a and b be these numbers.
1. If one number is 7 more than another, then
[tex]a-b=7.[/tex]
2. If the difference between numbers squares is 217, then
[tex]a^2-b^2=217.[/tex]
3. Solve the system of two equations:
[tex]\left\{\begin{array}{l}a-b=7\\a^2-b^2=217\end{array}\right.\Rightarrow \left\{\begin{array}{l}a-b=7\\(a-b)(a+b)=217\end{array}\right.\Rightarrow \left\{\begin{array}{l}a-b=7\\a+b=\dfrac{217}{7}=31\end{array}\right..[/tex]
Add these two equations:
[tex]a-b+a+b=7+31,\\ \\2a=38,\\ \\a=19.[/tex]
Then
[tex]19-b=7,\\ \\b=19-7=12.[/tex]
