<PRE><B>Question 1109206</B>
 a number is one less than twice another number,
a = 2b - 1
and the difference between their squares is 85.
a^2 - b^2 = 85
replace a with (2b-1)
(2b-1)^2 - b^2 = 85
FOIL (2b-1)(2b-1)
4b^2 - 2b - 2b + 1 - b^2 = 85
Combine to form a quadratic equation on the left
3b^2 - 4b + 1 - 85 = 0
3b^2 - 4b - 84 = 0
you can use the quadratic formula; a=3; b=-4; c=-84, but this will factor
(3b+14)(b-6) = 0
The positive integer solution
b = 6
Find a
a = 2(6) - 1
a = 11
:

 find the numbers 11, 6
:
:
Check: 
11^2 - 6^2 =
121 - 36 - 85 </PRE>