Solve x+y=5 & x^x+y^y=31 | Get Help Here

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The simultaneous equations x+y=5 and x^x+y^y=31 can be approached by substituting y with 5-x in the second equation. The resulting equation does not have a solution expressible in elementary functions, but it can potentially be solved using the Lambert W function. The confirmed solutions are x=3, y=2 and x=2, y=3, which satisfy both equations. These two pairs are likely the only solutions to the problem. The discussion emphasizes the limitations of solving such equations with standard methods.
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hey i need help with this its a simul eqn ,here it is ,
x+y=5,x^x+y^y=31.any help will be appreciated
 
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abia ubong said:
hey i need help with this its a simul eqn ,here it is ,
x+y=5,x^x+y^y=31.any help will be appreciated
Why do I feel I have seen this before? :rolleyes:

(2,3)

The Bob (2004 ©)
 
can i get a solution plssssssssssssssss
 
This is, after all, the second time you have posted this question: all I can do is give the same answer I did before: from x+ y= 5, y= 5- x so the second equation can be written xx+ (5-x)5-x= 31. That equation cannot be solved (for arbitrary right hand side) by any elementary functions. It is possible that such an equation can be solved by the "Lambert W function".

However, as was explained the last time this was posted, in this particular problem,
33+ 22= 31 so x= 3, y= 2 and x= 2, y= 3 are solutions. They are probably the only solutions. It shouldn't be too difficult to check that.
 

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