MHB How Can I Solve This Bilinear Integer Equation?

  • Thread starter Thread starter juantheron
  • Start date Start date
  • Tags Tags
    Integer
AI Thread Summary
The discussion centers on solving the bilinear integer equation 2x^2 - 3xy - 2y^2 = 7. The original poster attempts to factor the equation but makes an error in their factorization. A participant points out the mistake and suggests that the correct factorization should lead to integer solutions. They note that since the product of two integers equals 7, one must be ±1 and the other ±7. The conversation concludes with the original poster acknowledging the correction and seeking further assistance.
juantheron
Messages
243
Reaction score
1
If $x,y$ are integer ordered pair of $2x^2-3xy-2y^2 = 7,$ Then $\left|x+y \right| = $

My Try:: Given $2x^2-3xy-2y^2 = 7\Rightarrow 2x^2-4xy+xy-2y^2 = 7$

So $(2x-y)\cdot (x-2y) = 7.$

Now How can I solve after that

Help me

Thanks
 
Mathematics news on Phys.org
jacks said:
If $x,y$ are integer ordered pair of $2x^2-3xy-2y^2 = 7,$ Then $\left|x+y \right| = $

My Try:: Given $2x^2-3xy-2y^2 = 7\Rightarrow 2x^2-4xy+xy-2y^2 = 7$

So $(2x-y)\cdot (x-2y) = 7.$

Now How can I solve after that

Help me

Thanks


You are just a little bit off. You can check your work. Let's try that here.

$(2x-y)\cdot (x-2y) = 2x^2 - 4xy -xy + 2y^2 = 2x^2 -5xy + 2y^2 \neq 2x^2 - 3xy - 2y^2$.

Knowing this, what do you think the correct factorization is?
 
Once you have got the correct factorisation sorted out, notice that if the product of two integers is $7$, then one of them must be $\pm1$ and the other one must be $\pm7$.
 
Thanks Aryth, opalg Got it.
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Back
Top