I'm looking for alternative methods a question. My answer relies on a bit of guesswork and I don't think it's elegant, so I'm seeking other answers.

I'll post my solution in another post

Question

Let x and y be integers. Find the value of if

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- January 9th 2010, 07:53 PMI-ThinkAlternative methods
I'm looking for alternative methods a question. My answer relies on a bit of guesswork and I don't think it's elegant, so I'm seeking other answers.

I'll post my solution in another post

Question

Let x and y be integers. Find the value of if

- January 9th 2010, 08:05 PMI-Think
My solution

Fact 1) The L.H.S. must be a multiple of 3

Fact 2) If 0<y\leq{3}, then the R.H.S. is positive, but the L.H.S. is -ive, hence y>3

Fact 3) If y>22, a similar situation occurs, so 3<y<22

Fact 4) y cannot be a multiple of 3, as the L.H.S. would not be multiple of 3

Fact 5) I have stopped determining constraints and begun to guess the answer

Upon guessing, y=7 and x=2

So the value of follows - January 9th 2010, 08:24 PMwilder7bc
I think,

if you had 30x^2 + 517 could you not take x^2 to the other side?

and if you did and then divided (y^2) + (3x^2)(y^2)/(x^2)

Would that not cancel out the x2?

Giving you y^2 + (3)(y^2) = 30 + 517

??

I am probably breaking all kinds of rules but it seems that you loose x in that case and then you would have

4y^2 = 537

y^2 = 537/4

y = square root of (537/4)

I know I am all kinds of wrong I was just curious... Its ok to make a bit of fun of me I dont mind :P

Brian - January 9th 2010, 10:27 PMSoroban
Hello, I-Think!

Quote:

Let and be integers.

Find the value of if: .

We have: . .[1]

Since is an integer, must be a factor of 507.

The factors of 507 are: .

The only case in which is an integer is: .

Sustitute into [1]: .

Therefore: .