Finding Maximum Value of $e$ in $a,b,c,d,e \in R$

  • Context: MHB 
  • Thread starter Thread starter Albert1
  • Start date Start date
  • Tags Tags
    Maximum Value
Click For Summary

Discussion Overview

The discussion revolves around finding the maximum value of the variable \( e \) given the constraints \( a+b+c+d+e=8 \) and \( a^2+b^2+c^2+d^2+e^2=16 \). The context includes mathematical reasoning and exploration of potential values for \( e \) based on different assumptions about the other variables.

Discussion Character

  • Mathematical reasoning, Exploratory

Main Points Raised

  • Some participants propose specific values for \( a, b, c, d \) to calculate \( e \), such as \( a=b=c=d=2 \) leading to \( e=0 \), and \( a=b=c=d=1.2 \) resulting in \( e=3.2 \).
  • There is a repeated inquiry about the maximum value of \( e \) and whether it can be proven.
  • One participant references another's post as a potential solution, indicating a collaborative aspect to the exploration.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the maximum value of \( e \), and multiple approaches to the problem are presented without resolution.

Contextual Notes

The discussion does not clarify the assumptions behind the chosen values for \( a, b, c, d \), nor does it resolve the mathematical steps needed to definitively find \( e_{max} \).

Albert1
Messages
1,221
Reaction score
0
$a,b,c,d,e \in R$
$a+b+c+d+e=8$
$a^2+b^2+c^2+d^2+e^2=16$
$find :\,\, e_{max}$
 
Mathematics news on Phys.org
Albert said:
$a,b,c,d,e \in R$
$a+b+c+d+e=8$
$a^2+b^2+c^2+d^2+e^2=16$
$find :\,\, e_{max}$

[sp]
When a=b=c=d=2 we get e=0 and when a=b=c=d=1.2 we get e=3.2.
[/sp]
 
$e_{max}=?$
and can you prove it ?
 
My solution:

Because of the cyclic symmetry in the variables, we may let:

$$a=b=c=d$$

And so:

$$4a+e=8\implies a=\frac{8-e}{4}$$

$$4a^2+e^2=16$$

Substitute for $a$:

$$4\left(\frac{8-e}{4} \right)^2+e^2=16$$

This simplifies to:

$$e(5e-16)=0$$

Hence:

$$e_{\max}=\frac{16}{5}$$
 
Albert said:
$e_{max}=?$
and can you prove it ?

Yep. See MarkFL's post. :p
 

Similar threads

Graduate !?Puzzle?! -Possible Clue- Split the Difference
  • · Replies 12 ·
Replies
12
Views
1K
MHB Find a,b,c,d for Max $a+b-c+d$
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Difficult to understand the solution provided in the video (travelling salesman problem)
  • · Replies 3 ·
Replies
3
Views
2K
MHB (0,a) , (b,0) , (2,d) and (e,7) lie on y=2x+1, find a, b, d and e
  • · Replies 2 ·
Replies
2
Views
2K
MHB (Seemingly) Random Sequences
  • · Replies 7 ·
Replies
7
Views
2K
MHB What is the value of $(a+c)(b+c)(a-d)(b-d)$ given specific roots?
  • · Replies 6 ·
Replies
6
Views
1K
MHB Determine all possible values a/(a+b+d)+b/(a+b+c)+c/(b+c+d)+d/(a+c+d)
  • · Replies 2 ·
Replies
2
Views
2K
MHB The Minimum Value of a Quadratic Function: A Question of Symmetry
  • · Replies 3 ·
Replies
3
Views
2K
MHB What is the Value of \(2\tan\frac{1}{2}A\tan\frac{1}{2}B\) in Triangle ABC?
  • · Replies 2 ·
Replies
2
Views
1K
MHB Find Solutions to a+b+c+d=4, a^2+b^2+c^2+d^2=6, a^3+b^3+c^3+d^3=94/9 in [0,2]
  • · Replies 2 ·
Replies
2
Views
1K