Math Is Fun Forum

tony123

Member

Registered: 2007-08-03

Posts: 229

x is integer

if x is integer
find all integer x
such that
9x^2+160x+800
is a  perfect squer

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: x is integer

Let 9x[sup]2[/sup]+160x+800 = y[sup]2[/sup]. We may assume that y > 0.

Set 3y+9x+80 = k and solve these simulaneous equations in terms k:

You get

Since y > 0, [1] ⇒ k > 0. And k is a factor of 800. So all you need to do is try all the positive integer factors of 800 in [1] and [2] and see which ones give you integer solutions for x and y. You should find that there are only 6 of them: x = 2, −5, −7, −10, −14, −31.

Last edited by JaneFairfax (2007-09-01 10:47:59)

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: x is integer

Note: The trick I tend to use for such problems is to try and express the unknown(s) as a product of an integer. (In the problem above, I expressed them as a product of 800.) Then you just play around with the factors of the integer and try and solve for the unknowns.