Question

How can i solve 44y-yx = x^2 + 44x ?

Answer 1

for x and y, integer numbers ?

Answer 2

yes

Answer 3

http://www.wolframalpha.com/input/?i=44y-yx+%3D+x^2+%2B+44x

Answer 4

thanks

Answer 5

honestly, it is a math olympiad problem.....
honestly, i also want to going to do sport, now :)
i promise, i will write the answer here... because i got the answer, oke.

Answer 6

ok ok don't worry, i got what i needed, that was the simplified expression, i can work from there

Answer 7

i will exert my promise, and i hope u can understand what i was wrote ...
sorry, if my explaination doesnt be exactly and make u be not understanding, because honestly i cant speak english so well, my gramar and vocab so minim
let's start it :)
from ur equation, given 44y-yx = x^2 + 44x or
y(44-x) = x^2+44x
y = (x^2+44x)/(44-x) or
y = - (x^2+44x)/(x-44), by using division direct it can be
y = - ( x+88 + (3872/(x-44)) )
To get y integer, so x-44 must be the factors of 3872, are {+-1, +-2, +-4, +-8, +-11, +-16, +-22, +-32, +-44, +-88, +-121, +-176, +-242, +-352, +-484, +-968, +-1936, +-3872}, so there are 36 factors.
Therofore, the solution for x’s with x is an integer number satisfied :
For : x - 44 = +-1 ----- > x = 44 +- 1 , gives x = 43, x = 45
x - 44 = +-2 ----- > x = 44 +-2, gives x = 42, x = 46
x - 44 = +-4 ------> x = 44+-4, gives x = 40, x = 48
x - 44 = +-8 ----- > x = 44+-8, gives x = 36, x = 52
x - 44 = +-11 -----> x = 44+-11, gives x = 33, x = 55
x - 44 = +-16 -----> x = 44+-16, gives x = 28, x = 60
x - 44 = +-22 -----> x = 44+-22, gives x = 22, x= 66
x - 44 = +-32 -----> x = 44+-32, gives x = 12, x=76
x - 44 = +-44 -----> x = 44+-44, gives x = 0, x = 88
x - 44 = +-88 -----> x = 44+-88, gives x =-44, x = 132
x - 44 = +-121 -----> x = 44 +-121, gives x = -77, x = 165
x - 44 = +-176 -----> x = 44+-176, gives x = -132, x = 220
x - 44 = +-242 -----> x = 44+-242, gives x =-198, x = 286
x - 44 = +-352 -----> x = 44+-352, gives x = -308, x = 396
x - 44 = +-484 -----> x = 44+-484, gives x = -440, x = 528
x - 44 = +-968 -----> x = 44+-968, gives x = -924, x = 1012
x - 44 = +-1936 -----> x = 44+-1936, gives x = - 1892, x = 1980
x - 44 = +-3872 -----> x = 44+-3872, gives x = -3828, x = 3916
x’s has cleared but for y :)
The 2nd Round
To get the values of y, subtitute all x’s above to the equation :
y = - ( x+88 + (3872/(x-44)) )
for x = 43 gives y = 3741 --------> (43,3741)
for x = 45 gives y = - 4005 --------> (45,-4005)
for x = 42 gives y = 1806 --------> (42,1806)
for x = 46 gives y = - 2070 --------> (46,-2070)
for x = 40 gives y = 840 --------> (40,840)
for x = 48 gives y = - 1104 --------> (48,-1104)
for x = 36 gives y = 360 --------> (36,360)
for x = 52 gives y = - 624 --------> (52,-624)
for x = 33 gives y = 231 --------> (33,231)
for x = 55 gives y = - 495 --------> (55,-495)
for x = 28 gives y = 126 --------> (28,126)
for x = 60 gives y = - 390 --------> (60,-390)
for x = 22 gives y = 66 --------> (22,66)
for x = 66 gives y = - 330 --------> (66,-330)
for x = 12 gives y = 21 --------> (12,21)
for x = 76 gives y = - 285 --------> (76,-285)
for x = 0 gives y = 0 --------> (0,0)
for x = 88 gives y = - 264 --------> (88,-264)
for x = - 44 gives y = 0 --------> (-44,0)
for x = 132 gives y = -264 --------> (132,-264)
for x = - 77 gives y = 21 --------> (-77,21)
for x = 165 gives y = -285 --------> (165,-285)
for x = - 132 gives y = 66 --------> (-132,66)
for x = 220 gives y = - 330 --------> (220,-330)
for x = - 198 gives y = 126 --------> (-198,126)
for x = 286 gives y = - 390 --------> (286,-390)
for x = - 308 gives y = 231 --------> (-308,231)
for x = 396 gives y = - 495 --------> (396,-495)
for x = - 440 gives y = 360 --------> (-440,360)
for x = 528 gives y = - 624 --------> (528,-624)
for x = -924 gives y = 840 --------> (-924,840)
for x = 1012 gives y = - 1104 --------> (1012,-1104)
for x = - 1892 gives y = 1806 --------> (-1892,1806)
for x = 1980 gives y = - 2070 --------> (1980,-2070)
for x = - 3828 gives y = 3741 --------> (-3828,3741)
for x = 3916 gives y = - 4005 --------> (3916,-4005)
Thus, there are 36 order pairs (x,y) as the solutions, with x, and y is integer number
(By : Raden)

Answer 8

Wow, thank you very much

Answer 9

very welcome... HAPPY FUN :)