Question

The sum of the squares of two positive integers is 185. If one integer is 3 less than the other, fine the larger integer.

Answer 1

Answer:

$\boxed{\sf \ 11 \ }$

Step-by-step explanation:

Hi,

let's note the two integers a and b

$a^2+b^2=185 \ and \\\\a = b - 3$

We are asked to find b

replace a in the first equation

   $(b-3)^2+b^2=185\\\\b^2-6b+9+b^2=185\\\\ 2b^2-6b+9-185=0\\\\ 2b^2-6b-176=0\\\\ b^2-3b-88=0\\\\b^2+8b-11b-88=0\\\\b(b+8)-11(b+8)=0\\\\(b-11)(b+8)=0\\\\ b = 11 \ or \ b = -8$

As b must be a positive integer, the solution is 11

Hope this helps