$x + y = 5$ $x+y=5$ and $x^{y} + y^{x} = 17$ $x^y+y^x=17$ Find the value of $x and y$ $x and y$ ?

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Answer 1 · 2017-06-19T14:44:17

$x = 2, y = 3$ $x=2, y=3$
Assuming ${x,y} in NN$

Here we have two equations:

$x+y =5$

$x^y+y^x=17$

{Although there is no resaon to assume that $x$ and $y$ are naturals, it seemed like a sensible place to start.}

Assume ${x,y} in NN$

Since $x+y = 5$

$x in { 1, 2, 3, 4}$ and $y in {4, 3, 2, 1}$

Testing each $(x, y)$ pair in turn we notice that:

$2^3+3^2 = 8 + 9 =17$

Hence a solution to this system is $x=2, y=3$

NB: I have not worked through the cases where $(x, y) in RR$ , Hence, I have not proved that there are no other real solutions to this system.

x+y=5x+y=5x+y=5 and x^y+y^x=17xy+yx=17x^y+y^x=17 Find the value of x and yxandyx and y?