typical number theory sum

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here is a typical number theory problem. i hav tried this but was unable to solve this sum. i figured out the answer but could not proceed in any logical method. could you please tell me some logical step-by-step method for reaching the answer?

x^y+y^x=17
x+y=5
find x & y(both positive)
i request you to tell me the working of this problem not the answer.

#Mathematics #Algebra

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3 Answers

Lokesh Verma ·2009-05-17 20:28:21

This is not a very easy problem unless you allow for x and y to be integers

one method is to first say that x^y<17 given x+y=5

then find a upper limit on x and y.

Then proceed ..

But yeah you are right.. there is not a very good solution..

There is a similar question:
x+√y = 11
y+√x = 7

figure this out

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Ronald Clement ·2009-05-17 22:44:24

1st 1--

x=2 & y=3

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Ronald Clement ·2009-05-17 22:51:36

2nd one--

x=9 & y=4

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typical number theory sum

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