Solve-for-natural-numbers-x-2-y-2-x-y-3xy-

Question Number 149266 by mathdanisur last updated on 04/Aug/21

S o l v e f o r n a t u r a l n u m b e r s :

x^{2} + y^{2} + x + y = 3 x y

Answered by nimnim last updated on 04/Aug/21

\Rightarrow {(x + y)}^{2} + (x + y) = 5 x y

\Rightarrow (x + y) (x + y + 1) = 5 x y

f o r x, y \in N

c a s e . 1 x + y = x y a n d x + y + 1 = 5

\Rightarrow x + y = 4

\Rightarrow (x, y) = (2, 2)

c a s e . 2 x + y = 5 a n d x + y + 1 = x y

\Rightarrow (x, y) = (2, 3) o r (3, 2)

∴ s o l u t i o n s e t = {(2, 2), (2, 3), (3, 2)}

Commented by mathdanisur last updated on 04/Aug/21

T h a n k Y o u S e r

Commented by mathdanisur last updated on 04/Aug/21

S e r, b u t t h e r e a r e f i n i t e l y m a n y

s o l u t i o n s

Commented by mathdanisur last updated on 04/Aug/21

H o w c a n y o u e n s u r e t h e e q u a l i t y

w i l l b e a l w a y s o f t h e f o r m x y a n d 5 ?