Answer:
[tex]\boxed{\sf \ 11 \ }[/tex]
Step-by-step explanation:
Hi,
let's note the two integers a and b
[tex]a^2+b^2=185 \ and \\\\a = b - 3[/tex]
We are asked to find b
replace a in the first equation
[tex](b-3)^2+b^2=185\\\\<=>b^2-6b+9+b^2=185\\\\<=> 2b^2-6b+9-185=0\\\\<=> 2b^2-6b-176=0\\\\<=> b^2-3b-88=0\\\\<=>b^2+8b-11b-88=0\\\\<=>b(b+8)-11(b+8)=0\\\\<=>(b-11)(b+8)=0\\\\<=> b = 11 \ or \ b = -8[/tex]
As b must be a positive integer, the solution is 11
Hope this helps
