Help me, thanks!

Question

The difference between two positive integers is 6. If the smaller is added to the square of the larger, the sum is 104 . Find the integers by solving the equation.

Answer 1

x, y - two integers

x^2 + y = 104

x - y = 6

add two equations:

x^2 + x = 110

x^2 + x - 110 = 0

(x + 11)(x - 10) = 0

x = -11 or 10

if x = 10, because x - y = 6, then 10 - y = 6 and y = 4. also (10)^2 + 4 = 104, so x = 10, y = 4 is a solution

If you try for x = - 11 you will find that the x,y values are not a solution.