
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
 LinkBack  Thread Tools  Display Modes 
January 2nd, 2019, 12:50 PM  #1 
Newbie Joined: Jan 2019 From: gd Posts: 1 Thanks: 0  Inequality problem
Let triangle with side a,b,c such that a+b+c=10. Prove this in.png I need help with this problem by use of triangle inequality, AG or similar inequality that I know. So I ask for hint. Last edited by skipjack; January 3rd, 2019 at 06:42 AM. 
January 2nd, 2019, 01:15 PM  #2  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,302 Thanks: 960 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
So: $\displaystyle a + b + c = 10$ Here's the inequality in the image: $\displaystyle a^2 + b^2 + c^2 + \frac{2}{5} abc < 50$ Can we take it that you have to derive the inequality from the first equation? Dan Last edited by skipjack; January 3rd, 2019 at 06:44 AM.  
January 2nd, 2019, 06:04 PM  #3 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond 
I've posted the image inline.

January 2nd, 2019, 06:23 PM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond 
Because the variables in the inequality can be interchanged with respect to value and position the equation has cyclic symmetry and an extremum is reached when all three sides are equal. After you come up with a value for that all you have to do is devise another triangle to show that the LHS of the inequality is less than the previously calculated value.

January 3rd, 2019, 08:03 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 21,026 Thanks: 2257  

Tags 
problem 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Inequality problem  Chris A  Algebra  3  May 12th, 2015 02:56 AM 
Inequality problem  itiffanysphone  Algebra  6  December 10th, 2014 08:13 AM 
Inequality problem  wawar05  Number Theory  1  October 24th, 2012 08:49 AM 
Inequality problem  Havoc  Math Events  2  October 26th, 2010 08:15 AM 
i have problem with an inequality  kokusaka  Algebra  0  September 30th, 2008 07:45 AM 