+1855 If $a$ and $b$ are positive integers for which $ab - 3a + 4b = 131$, what is the minimal possible value of $|a - b|$?
+1950 We can use a really simple and cheeky trick to solve this problem.
Taking the product of the coeffiicents of a and b and add this to both sides, we get
ab−3a+4b+(4∗−3)=131+(4∗−3)ab−3a+4b−12=119
Factoring the left side of the equation, we get
(a+4)(b−3)=119
Now, we take the two factros with the smallest margin, 7 and 17. We have
(13+4)(10−3)→|a−b|=|13−10|=3
So 3 is our answer.
Thanks! :)
+1950 We can use a really simple and cheeky trick to solve this problem.
Taking the product of the coeffiicents of a and b and add this to both sides, we get
ab−3a+4b+(4∗−3)=131+(4∗−3)ab−3a+4b−12=119
Factoring the left side of the equation, we get
(a+4)(b−3)=119
Now, we take the two factros with the smallest margin, 7 and 17. We have
(13+4)(10−3)→|a−b|=|13−10|=3
So 3 is our answer.
Thanks! :)
