MHB What Is the Maximum Value of \(a^2+ab+2b^2\) Given \(a^2-ab+2b^2=8\)?

  • Thread starter Thread starter anemone
  • Start date Start date
  • Tags Tags
    Maximum
AI Thread Summary
The problem involves maximizing the expression \(a^2 + ab + 2b^2\) under the constraint \(a^2 - ab + 2b^2 = 8\) with \(a\) and \(b\) as positive real numbers. Participants discuss various methods to approach the maximization, including substitution and optimization techniques. One user successfully finds the maximum value and is encouraged to share their solution process for clarity and learning. The discussion emphasizes the importance of showing work in mathematical problem-solving.
anemone
Gold Member
MHB
POTW Director
Messages
3,851
Reaction score
115
$a$ and $b$ are positive real numbers such that $a^2-ab+2b^2=8$.

Find the maximum value of $a^2+ab+2b^2$.
 
Mathematics news on Phys.org
Here:

$\frac{4}{7}(4+\sqrt2)^2$
 
conscipost said:
Here:

$\frac{4}{7}(4+\sqrt2)^2$

Your answer is correct, conscipost! (Yes) Well done!

But I'd appreciate it if you show your solution (but not merely the final answer) so we know what approach you used, sounds good to you?
 
Thread 'Video on imaginary numbers and some queries'

Thread 'Video on imaginary numbers and some queries'

Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
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 »
Thread 'Unit Circle Double Angle Derivations'

Thread 'Unit Circle Double Angle Derivations'

Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...
View full post »

Similar threads

MHB Given a,b∈T, a^2−ab+b^2 divides a^2b^2, Prove that T is finite
Replies
2
Views
1K
MHB What is the maximum value of $a^2b$?
Replies
10
Views
3K
MHB Can I Factor 4a^2b^2 - 9(ab + c)^2?
Replies
4
Views
1K
MHB Find Integer Solutions to $k=\dfrac{ab^2-1}{a^2b+1}$
Replies
1
Views
1K
MHB Find the sum of all values of positive integer a
Replies
1
Views
1K
MHB Minimum of $a$ for $a^2+2b^2+c^2+ab-bc-ac=1$
Replies
1
Views
1K
MHB Min Value of $\dfrac{a+3c}{a+2b+c}$+$\dfrac{4b}{a+b+2c}$+$\dfrac{8c}{a+b+3c}$
Replies
1
Views
2K
Find the values of a and b to get max/min of certain expression
Replies
21
Views
3K
I Uncovering the Mystery of Calorie Constants
Replies
1
Views
1K
MHB High school inequality 2 |x^2y-a^2b|<A
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top