Question

How many pairs (a, b), where a and b are positive integers, satisfy the equation a2−b2=105? PLS HELP

Answer 1

Answer:

  4

Step-by-step explanation:

The left side of the equation can be factored as the difference of squares:

  (a -b)(a +b) = 105

The right side of the equation can be factored to 4 different pairs of factors:

  105 = 1·105 = 3·35 = 5·21 = 7·15

For each of the factor pairs, we can match factors to get, for example, ...

  a -b = 1

  a +b = 105

The solution to this is a = (105 +1)/2 = 53, b = (105 -1)/2 = 52. Thus, we have ...

  (a, b) = (53, 52)

For the other factor pairs, the solutions are ...

  (a, b) = (19, 16), (13, 8), (11, 4)

There are a total of 4 positive integer solutions.