If a and b are integers such that a2 − b2 = 100, what is the greatest possible value of a?

26

Step-by-step explanation:

Question says that 'a' and 'b' are integers that implies we cannot have 'a' and 'b' in the form of decimals.

Now, lets expand the given equation:

Lets say: ,

Let us consider the factor pairs of 100.

Only factor pair gives us the integer values of 'a' and 'b'.

....equation  (1)

........ equation (2)

adding equation 1 and 2, we get:

Plugging the value of 'a' in the equation 2

So the greatest possible value of 'a' is 26.