How do you solve this?

Question

a+b+c=x
abc=y
a^b^c=z

What does a, b, and c equal?

Assume that I already know what x, y, and z are. I want "a" to be the same in all three equations, as well as "b" and "c". When "a", "b", and "c" are solved for, they should make all of the equations true.

By a^b^c, I mean (a^b)^c.

Answer 1

Try this:
a+b+c=x.........then changing things around, a=x-b-c

Now the next formula.

abc=y...............or we could say.....b=y/ac

Now combine......(x-b-c)(y/ac)c=y.....or (xc-bc-c^2)=a

You can plug the new above formulas to the next formula.

a^b^c=z......(xc-bc-c^2)^b^c=z

With this we have:

a=c root of the b root of z

b= c root of z/ (xc-bc-c^2)

c= the b root of the (xc-bc-c^2) root of z

This is the best solution I can come up with considering the problem. Try to reduce them more if you can.

Answer 2

Well, I can find a particular solution for you.
Let's let c =1. Then we can take a=b=2 in all 3 equations.
So this gives
2 + 2 + 1 = 5
2*2*1 = 4
(2^2)^1 = 4
I don't know if there are any other integer solutions.
Will play with it and see.

Answer 3

also note that (a^b)^c is not the same as a^(b^c), so you should specify what you mean by a^b^c.
(example: (2^2)^3 = 64 while 2^(2^3) = 256 )

Answer 4

How do "a", "b" and "c" relate to each other?

Knowing "x", "y" and "z" is not enough. There has to be some clue or relationship for the others. Substitution is impossible without it.

Answer 5

You do not have enough information to solve this system.

Answer 6

theres not anough info to figure it out

Answer 7

go and ask my friend ALBERT
Hahahah!

Answer 8

Shitforbrains.