Question

If a and b are integers such that a^2 - b^2 = 100, what is the greatest possible value of a?

Answer 1

The greatest possible value of integer a, for the equation
`a^2 - b^2 = 100`, is 10. This is derived by choosing the smallest integer value for b, which is 0, allowing a to be as large as possible.

Step-by-step explanation:

The student has asked for the greatest possible value of a if a and b are integers such that a2 - b2 = 100. This can be factored into a difference of squares: (a + b)(a - b) = 100. Since we want the greatest possible value of a, we need to find the smallest absolute value for b, so that a can be as large as possible. If we let b = 0, then a2 = 100 and so the greatest possible integer value of a is 10.

Answer 2

the maximum value of a is 10, when b is 0