# Thread: straight line and function

1. ## Re: straight line and function

thank you ebaines,

now the answer is complete , please look at this

2. ## Re: 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?

3. ## Re: straight line and function

Originally Posted by ebaines
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?
that is

4. ## Re: 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.

5. ## Re: 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?

6. ## Re: 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

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