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Topic review (newest first)
- ganesh
- 2005-08-01 19:03:13
Corrected the post; thanks, Mathsyperson. 
- mathsyperson
- 2005-08-01 18:54:52
ganesh wrote:
Put x=2,
we get 4y² + y - 14 = 0, Solving,
we get y = [-1 ± √(1 + 224)] / 2
y=[-1 ± √(1 + 224)]/8, actually. That means that y=-2 or 1.75 and the original proof wanted x and y to both be natural, meaning that these values are disregarded. The same applies to your second post where x=1. Sorry!
- ganesh
- 2005-08-01 16:36:24
MathsIsFun wrote:
Let's plug in some numbers just to get this started:
x=1: 3x^2 + x = 4y^2 +y becomes 5 = 4y^2 +y
When we put x=1,
3x² + x = 3(1² ) + 1 = 4
Therefore,
4y² + y - 4 = 0
y = [-1 ± √ (1 + 64)]/8 = [-1 ± √ 65 ]/8
which is an irational number.
We see that here too x-y is not the square of a natural number
- ganesh
- 2005-08-01 16:21:00
juki wrote:
x and y are two natural numbers such that 3x^2 + x = 4y^2 +y
Put x=2,
we get 4y² + y - 14 = 0, Solving,
we get y = [-1 ± √(1 + 224)] / 8
y = -2 or 1.75
Neither of them are Natural Numbers!
x - y is NOT always a square of a natural number 
- kylekatarn
- 2005-07-31 21:41:52
Another question - has this been already proved or did you toss a random problem?
If its random maybe we should try to disprove first.
- MathsIsFun
- 2005-07-31 15:19:34
Thanks for the puzzle, juki.
Oh, and kyle, I just added the "∈" up top, so you can use that if you want
(BTW kylekatarn is confirming: "is x and y a Natural Number {1,2,3,4,...} and is n an integer {... -3, -2, -1, 0, 1, 2, 3, ...} ?")
Let's plug in some numbers just to get this started:
x=1: 3x^2 + x = 4y^2 +y becomes 5 = 4y^2 +y
4y^2 +y - 5 = 0 has the solutions 1 and -1.25
Now, -1.25 is not included because y should be a Natural Number, so we are left with
x=1, y=1, and x-y=0, so I suppose 0 is the square of 0, so that is a good start.
- kylekatarn
- 2005-07-31 12:38:50
is this what we need to prove?
(x,y)∈N and 3x² +x=4y² +y => x-y=n² and n∈Z
//Mathisfun - Thanks for adding the symbol '∈'!
- juki
- 2005-07-31 00:00:29
1. x and y are two natural numbers such that 3x^2 + x = 4y^2 +y . Prove that x - y is the square of a whole nnumber rate this problem from 0 to 10 and tell ur soloution