who are good in math?

Question

a^2-b^2 = 33
a^3-b^3= 817

what is a+b equal to

Answer 1

will be 11

Answer 2

CTU vs FBi's answer is wrong!!
The answer is a+b= 33.
Proof:
a²-b² = (a-b)(a+b) = 33 = 3*11
a³-b³ = (a-b)(a²+ab+b²) = 817 = 19*43
Since a-b is a common factor of these 2 numbers
and they are relatively prime,
we must have a-b = 1.
But then a +b = 33
...............a - b = 1
So a = 17 and b = 16
and a² + 2ab + b² = 289 +272 + 256 = 817.
So a+b = 33 is the correct answer.

Answer 3

24.8