Try to do it in shortest time

hey_thr67 wrote:When the sqare of a number and the cube of a smaller number are added the result is 593. If the square of the smaller number exceeds the bigger number by 55, find the difference of the two numbers.

A: 1
B: 2
C: 3
D: 4
E: 7

Let A be the bigger number and a be the smaller number.

A^2 + a^3 = 593 -- (1)
a^2 - A = 55 -- (2)

The following values satisfy the second equation:
a = 8, A = 9 (we start with a = 8 because that is first square value that exceeds 55)
and
a = 9, A = 26
and so on.

a = 8, A = 9 satisfies the first equation also.
A - a = 1

[spoiler](A)[/spoiler] is correct.