MHB Find Lowest Value for A: a1, a2, a3 & 4 | Arithmetic Progression

AI Thread Summary
The discussion focuses on finding the lowest value of A = a1a2 + a2a3 + a3a1 for an arithmetic progression defined by a1, a2, a3, and 4. A participant expresses uncertainty about their approach, having derived A = 3x^2 + 6xd + 2d^2. Another user suggests that the fourth term of the progression can simplify A into a single variable, which would facilitate finding the minimum value. The original poster acknowledges the oversight and appreciates the guidance provided. The conversation emphasizes the importance of utilizing all given terms in mathematical problems for simplification.
mitaka90
Messages
9
Reaction score
0
a1, a2, a3 and 4 make an arithmetic progression with difference d. For which values of d, A = a1a2 + a2a3 + a3a1 has the lowest value?I don't know if I went with the right approach, but I managed to get this : A=3x2 +6xd + 2d2 for a1= x, a2 = x + d, etc... But I don't know what else to do.
 
Mathematics news on Phys.org
mitaka90 said:
a1, a2, a3 and 4 make an arithmetic progression with difference d. For which values of d, A = a1a2 + a2a3 + a3a1 has the lowest value?I don't know if I went with the right approach, but I managed to get this : A=3x2 +6xd + 2d2 for a1= x, a2 = x + d, etc... But I don't know what else to do.
Hi mitaka90!

It seems to me you haven't made good use of the given fourth term in that arithmetic progression...:) the fourth term would help you to simplify your $A$ in terms of only one variable and when you have the quadratic equation in terms of one variable, I believe you could handle from there...
 
anemone said:
Hi mitaka90!

It seems to me you haven't made good use of the given fourth term in that arithmetic progression...:) the fourth term would help you to simplify your $A$ in terms of only one variable and when you have the quadratic equation in terms of one variable, I believe you could handle from there...

Omg, I'm such a moron. I hate it when I do the hard work and then the easiest and most noticable thing just slips from my sight. Thank you sincerely, I guess that little tip is what I needed.
 

Thread 'Non-orthogonal bases'

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...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

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...
View full post »

Similar threads

MHB Sum of First 20 Terms of Arithmetic Progression with Even Terms Removed
Replies
7
Views
2K
MHB A problem on arithmetic progressions.
Replies
6
Views
2K
How to Solve Arithmetic Sequence Problems
Replies
1
Views
1K
I Newton Divided Difference Interpolation Polynomial
Replies
1
Views
3K
MHB Show that the number of questions he answered is 14, Arithmetic progressions
Replies
2
Views
1K
Comp Sci An Introduction to Deep Learning and Modifying Code
Replies
7
Views
2K
Formulas for Arithmetical and Geometrical Progression
Replies
17
Views
2K
Area between two curves (x = cos(y) and y = cos (x))
Replies
5
Views
2K
Another arithmetic progression problem
Replies
4
Views
2K
Solving for nC8,nC9, and nC10 in an Arithmetic Progression
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top