Register to reply

Solve for x,y

by arka.sharma
Tags: solve
Share this thread:
Jan9-14, 04:06 AM
P: 7
Hi All,

I was given two equations back in my school days to solve for both x and y it is as follows

x^y = y^x & x+y = 6

Now it can be seen that following would be possible solutions (x=4,y=2),(x=3,y=3),(x=2,y=4).
But is there any deductive way to solve this ?

Phys.Org News Partner Mathematics news on
Heat distributions help researchers to understand curved space
Professor quantifies how 'one thing leads to another'
Team announces construction of a formal computer-verified proof of the Kepler conjecture
Jan9-14, 04:49 AM
PF Gold
P: 375
Solving (6-y)^y == y^(6-y)
Which can be represented graphically.
Jan10-14, 03:58 AM
P: 7
Thanks for your reply. But how to solve the equation (6-y)^y == y^(6-y) ?

Jan10-14, 06:54 AM
PF Gold
P: 375
Solve for x,y

Put the RHS and the LHS of the equation on a graphic and see where these curve cut each other.
You will find the root that you already know.
If there are other roots, you will likely find out.
Afterward, you might find out arguments to "prove" you found all the roots.
The graphical representation will help a lot.
Jan10-14, 09:28 AM
Sci Advisor
PF Gold
P: 39,563
Quote Quote by arka.sharma View Post
Thanks for your reply. But how to solve the equation (6-y)^y == y^(6-y) ?
You were told to solve it graphically. It can also be solved using a numerical iteration method. If you are looking for an elementary algebraic way of solving it, there is none.

Register to reply

Related Discussions
Sin(ax+b)=c, solve for x Precalculus Mathematics Homework 3
Solve |3x-7|-|x-8| > 4 (solve algebraically) Precalculus Mathematics Homework 6
I forgot how I can solve this... Like this example:Solve for the Calculus 2
How do you solve problem you cannot solve? Academic Guidance 16
HOw to solve this? Differential Equations 4