Given that x, y are natural numbers, x > y and satisfy (x + y) + (x + xy-y) + X / y = 243, find the value of X + y

x=24,y =8,x+y = 32
or
x=54,y = 2 ,x+y = 56
According to x > y
（x+y）+（x+xy-y)+ x/y=243
X / y has no remainder
So there is a positive integer K
x = ky
(x + y) + (x + xy-y) + X / y = 243 substituted by x = KY
(ky +y) + (ky +ky^2 -y) +k = 243
2ky + k y^2 +k = 243
k(y+1)^2 = 243
(y+1)^2 = 243/k
So K can be divided by 243
243 = 3*3*3*3*3
After preserving the complete square 3 * 3 or 9 * 9, 3 or 27 are further divided by K
So k = 3; y = 9-1 = 8, x = KY = 24
Or K = 27; y = 3-1 = 2, x = KY = 54
So x + y = 32 or x + y = 56

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