thank you ebaines,

now the answer is complete , please look at this

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- May 8th 2013, 02:34 AMabualabedRe: straight line and function
thank you ebaines,

now the answer is complete , please look at this - May 8th 2013, 04:33 AMebainesRe: straight line and function
That's fine as far is goes, but of course is not a complete proof. I assume you have worked out a proof of the statement that the difference of two squared odd numbers must be divisible by 8, right?

- May 8th 2013, 07:44 AMabualabedRe: straight line and function
- May 8th 2013, 08:26 PMibduttRe: straight line and function
I like it is a very interesting discussion. I think we can approach the question as under:

let a = 2m+1, b = 2n +1 and c= 2p +1

now discriminant of bx^2 + ax + c = 0 is D = a^2 - 4 bc = ( 2m+1)^2 - 4 ( 2n +1) ( 2p+1) = 4m^2 + 4m + 1- 4 [ 4 np + 2 (n+p) +1 ]

= 4m^2 + 4m - 4 [ 4 np + 2 (n+p) ] - 3 = 4 [ m^2 + m - 4 np - 2 (n+p) ] - 3

Now we observe that it is not a perfect square. Thus the roots will be irrational. - May 13th 2013, 01:55 AMabualabedRe: straight line and function
hi. ibdutt

how did you know that 4 [ m^2 + m - 4 np - 2 (n+p) ] - 3 is not a perfect square? - May 13th 2013, 04:30 AMibduttRe: straight line and function
It has three variables m , n and p.

the expression for ( a+b+c)^2 = a^2+b^2+c^2 + 2ab + 2bc + 2 ca

that is why