My Math Forum  

Go Back   My Math Forum > College Math Forum > Number Theory

Number Theory Number Theory Math Forum

LinkBack Thread Tools Display Modes
April 12th, 2015, 04:38 PM   #1
Joined: Dec 2012

Posts: 12
Thanks: 0

Pythagorean and Quadratic equation Proof

Hello Everyone,
I had a midterm in an mathematical econ class and we had to come up with a proof for the following question It was with regards to 2nd order difference equations, so Y(t+2) means Y subscript t+2:

Show that for Y(t+2)+aY(t+1)+bY(t)=2, if 1+a+b=0 then it is always true that one of the roots of this equation is always equal to 1.

The solution the professor came up with was: 1+a+b=0 then b=-1-a. therefore
quadratic/characteristic equation shows that [-a+-sqrt(a^2-4(1)(-1-a))]/2(1)
simplifies to [-a+or - a+2]/2. this shows that at least one of the roots will always be 1.

My proof was slightly different. if 1+a+b=0 then a+b=-1, so for any values of a or b, using the quadratic equation [-a+-sqrt(a^2-4(b))]/2 this solves so that root 1=2/2 and root 2=some value/2.

What I noticed was that using these parameters, the terms within the square root expression always follow the pythagorean theorem rule. Further more, the value inside the square root term is always +1 greater than the absolute value of the higher variable. However, I haven't been able to express the relationship. I'm hoping one of you who happen to be good at proofs can both flesh out my proof properly and explain the relationship to me mathematically. I couldn't find anything online.
I am attaching a quick proof that I wrote, in case that helps.
Attached Images
File Type: jpg IMAG1116.jpg (86.3 KB, 3 views)
HenryMolaison is offline  

  My Math Forum > College Math Forum > Number Theory

equation, proof, pythagorean, quadratic

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Help on Pythagorean Proof modus1985 Trigonometry 7 December 19th, 2014 09:44 PM
quadratic equation Alexis87 Algebra 3 July 31st, 2013 05:56 AM
simplify equation to get a quadratic equation mich89 Algebra 3 January 9th, 2013 01:22 PM
Primitive Pythagorean Proof question.! eChung00 Number Theory 2 September 10th, 2012 05:13 PM
Quadratic irrational proof Stuck Man Number Theory 1 February 10th, 2012 04:44 AM

Copyright © 2019 My Math Forum. All rights reserved.