How many pairs of integers (x,y) are there such that 2x2−2xy+y2=225?

Question

anonymous · Answer

2x2−2xy+y2=225
x^2 + (x-y)^2 =225

anonymous · Answer

15^2 + 0^2 = 225
=>x = 15 AND x-y=0
Thus, x=15 and y=15

anonymous · Answer

12^2 + 9^2 =225

anonymous · Answer

=> x=12 AND x-y=9 
Thus, x=12 and y=3
Now,
9^2 + 12^2 =225
=>x=9 and x-y=12
So, x=9 and y=-3

anonymous · Answer

So, looks likes 
(15,15) , (12,3) and (9,-3)
are the only solutions

anonymous · Answer

no i think there will be more number of solutions are available  for this equation

anonymous · Answer

(-15,-15) , (-12 , -21) , (-9,-21)

anonymous · Answer

0^2 + 15^2 =225
0^2 + (-15)^2=225
15^2 + 0^2=225
(-15)^2 + 0^2 =225
(12)^2 + (9)^2=225
(-12)^2+(9)^2=225
(12)^2 + (-9)^2=225
(-12)^2 + (-9)^2=225
(9)^2 + (12)^2 =225
(-9)^2+(12)^2=225
(9)^2+(-12)^2=225
(-9)+(-12)^2=225

sirm3d · Answer

$$\large x^2+(x-y)^2=225$$ and $$\large 9^2+12^2=15^2$$ so there are the possibilities:$$\large x=\pm 9 \text { and } x-y = \pm 12$$ $$\large x=\pm 12 \text { and } x-y = \pm 9$$ and the trivial cases \large [x=0\] and $$\large x= \pm 15$$

anonymous · Answer

Looks like 12 solutions

anonymous · Answer

thank u 12 is correct

anonymous · Answer

yw