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Solve for x,yby arka.sharma
Tags: solve 
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#1
Jan914, 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 ? Regards, Arka 


#2
Jan914, 04:49 AM

PF Gold
P: 377

Solving (6y)^y == y^(6y)
Which can be represented graphically. 


#3
Jan1014, 03:58 AM

P: 7

Thanks for your reply. But how to solve the equation (6y)^y == y^(6y) ?



#4
Jan1014, 06:54 AM

PF Gold
P: 377

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. 


#5
Jan1014, 09:28 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,693




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