Solve-simultaneously-x-x-y-y-31-x-y-5-Please-i-did-workings-Thanks-for-your-help-

Question Number 5386 by sanusihammed last updated on 12/May/16

S o l v e s i m u l t a n e o u s l y

x^{x} + y^{y} = 31

x + y = 5

P l e a s e i d i d w o r k i n g s \dots

T h a n k s f o r y o u r h e l p .

Commented by Rasheed Soomro last updated on 12/May/16

Trying to find out the solution in

natural numbers :

Possible solutions for x + y = 5

are (1, 4), (2, 3), (3, 2), (4, 1)

Substituting one by one in x^{x} + y^{y} = 31

we will find that only (2, 3) and (3, 2)

satisfy the equation :

2^{2} + 3^{3} = 4 + 27 = 31 and

3^{3} + 2^{2} = 27 + 4 = 31

Hence (2, 3) and (3, 2) are solutions .

Commented by sanusihammed last updated on 12/May/16

P l e a s e n o a l g e b r a l s o l u t i o n ?

Commented by Rasheed Soomro last updated on 12/May/16

x + y = 5 \Rightarrow x = 5 - y \Rightarrow x^{x} = {(5 - y)}^{5 - y}

\Rightarrow x^{x} + y^{y} = {(5 - y)}^{5 - y} + y^{y} = 31

I think only numerical methods!