a+b=23?

[cwarn23]

Hi and sorry if this is the wrong forum but didn't know where to place my question. I need to know the answer of a+b=23. So how would I calculate the values of a and b and the same would apply for a^b=16. So basically I need to know the algebraic equation to find the original numbers. Does anybody know where I can find such a formula as I am trying to reverse a formula. Thanks...

[Rashakil Fol]

If a + b = 23 and a^b = 16, well, you know that a = 23 - b, which means (23 - b) ^ b = 16.

So here's what you should do. Write (23 - b) ^ b - 16 = 0, and then use Newton's method to find the zero of that equation. You know how to differentiate (23 - b) ^ b, right? Haha, that's one of the harder ones. Good luck.

[cwarn23]

The equations a+b and a^b were two separate questions. So do you know how I would solve that?

[Rashakil Fol]

If they're separate questions then each question has infinitely many solutions. And it should be pretty obvious, if you know the basics of [s]algebra[/s] obviosity.

[mrnutty]

>> a+b=23

Not taking into account floating points and just positive natural numbers. Then

if b > 23 then no Answer Possible
if b = 23, then a = 0;
if b = 22, then a = 1
if b = 22, then a = 2

General Equation : B = 23 - a OR A = 23 - b

Following this pattern b could be from 23 - 0 and a could be from 0 - 23
So there are 2 * 23 = 46 different solutions.

If thats not it then clear up what you want.