#algebra ordered pair
white salmon
blissful plinth
is this asking you to find the number of ordered pairs in Q^2, or...?
or Z^2 more likely
white salmon
I’m not getting your question
blissful plinth
like
there are infinitely many solutions
well, maybe that's the answer which i just spoiled for you
white salmon
Oh I forgot to write that they must be integers
wheat wedge
Hm, looks interesting.
blissful plinth
Oh I forgot to write that they must be integers
ah yes
alr
so you can rewrite as
x^2 + (x-y)^2 = 289
that might help you
white salmon
Ye I got that eqn but it got really complicated as I was getting 4 values of X and four values of X-y
blissful plinth
hm
what values did you get
wheat wedge
We have:
x^2 + (x^2 - 2xy + y^2) = 289
x^2 + (x - y)^2 = 289
Now, note that 289^2 = 17^2 = 8^2 + 15^2. So, you can make 8 systems of equations.
Actually, hold on, might be more than 8.
blissful plinth
i think it is
white salmon
X= +-64 and X=+-225 and X-y = +64 and X-y =+-225
blissful plinth
X= +-64 and X=+-225 and X-y = +64 and X-y =+-225
there is also X = 289
and X = 0
wheat wedge
(x, x - y) can be...
(±17, 0)
(0, ±17)
(±8, ±15)
(±15, ±8)
(±8, ∓15)
(±15, ∓8)
So, 12 systems.
wheat wedge
But the ordered pair must be in the form of (X,y)
A system x = a, x - y = b will only have 1 solution.
So, for each pair (x, x - y) there's a unique pair (x, y).
And, considering that both will be integers, all 12 systems should give an integer solution.
wheat wedge
No worries! You just need some practice.
white salmon
yea anyways thanks for your help
wheat wedge
You're welcome!