Answer:
12 and 17
Step-by-step explanation:
Let the two integers be m and n
[tex]m - n = 5[/tex]
[tex]m^2+n^2=433[/tex]
From the first equation,
[tex]m=5+n[/tex]
Substitute this in the second equation.
[tex](5+n)^2+n^2=433[/tex]
[tex]25+10n+n^2+n^2=433[/tex]
[tex]25+10n+2n^2=433[/tex]
[tex]2n^2+10n-408=0[/tex]
Divide both sides 2
[tex]n^2+5n-204=0[/tex]
Factorise to get
[tex](n-12)(n+17)=0[/tex]
Therefore, [tex]n=12[/tex] or [tex]-17[/tex]
But [tex]n[/tex]is a positive integer. Therefore [tex]n=12[/tex]
From the first equation,
[tex]m-n =5[/tex]
[tex]m-12 =5=17[/tex]
The two integers are 12 and 17.
Let's check
17 - 12 = 5
[tex]17^2+11^2 = 289 + 144 = 433[/tex]
