One positive integer is 3 less than twice another. the sum of their squares is 233. find the integers.

Let the two integers be x and y
x-3= 2y
x=2y+3(1)

x²+y²= 233(2)
sub eqn (1) into (2)
{2y+3}²+y²=233
4y² + 12y +9 +y²=233
5y²+12y+9-233=0
5y²+12y-224=0
y= -8 or 5.6
recall they are positive integers so y=5.6
now sub y=5.6 into eqn (1)
x=2(5.6)+3 = 11.2+3=14.2

the two integers are 14.2 and 5.6