SOLUTION: (((Please give me a step wise solution for equation x^y+y^x=1061)))

Question 157633: (((Please give me a step wise solution for equation x^y+y^x=1061)))
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
You can iterate to find solutions.
Start with x=0.

No solution at x=0.
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Next x=1/2.

Actually, y becomes large and the term goes to zero, so the equation looks like,
and
y=1061*1061=1125721
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Next x=1. That's an easy one.

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Next x=2,

Here's where the iteration takes place.
I set up an EXCEL spreadsheet to home in on a solution.
and

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Next x=3,

Here's where the iteration takes place.
I set up an EXCEL spreadsheet to home in on a solution.

Looks like there's only one solution.
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(1/2,1125721)
(1,1060)
(2,-32.572)
(2,9.911)
(3,6.12)
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Hope it helps.
Good luck.
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