My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
November 18th, 2018, 10:00 AM   #1
Member
 
Joined: Oct 2012

Posts: 70
Thanks: 0

minimum value

Let a,b,c and d to be a positive real. Such that:
(a+b)(c+d)=143
(a+c)(b+d)=150
(a+d)(b+c)=169.
Find the min value of a^2+b^2+c^2+d^2?
fahad nasir is offline  
 
November 18th, 2018, 12:20 PM   #2
Senior Member
 
romsek's Avatar
 
Joined: Sep 2015
From: USA

Posts: 2,203
Thanks: 1157

Applying the method of Lagrange Multipliers using 3 constraint equations

and with the help of software to churn through the considerable algebra

I come up with the only value of the sum of the squares of a,b,c,d

that also satisfies the constraints is $a^2 + b^2 + c^2 + d^2 = 214$.

Are you familiar with how to use Lagrange Multipliers?

There may be some much simpler method.

Last edited by romsek; November 18th, 2018 at 12:30 PM.
romsek is online now  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
minimum



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Help with this minimum... 3uler Calculus 3 November 23rd, 2014 08:08 AM
Difference Between Maximum/Minimum Value and Maximum/Minimum Turning Point Monox D. I-Fly Pre-Calculus 4 October 13th, 2014 06:58 AM
Minimum value proglote Algebra 13 April 29th, 2011 06:46 PM
minimum value ely_en Algebra 9 October 25th, 2009 06:59 PM
Minimum value of D K Sengupta Number Theory 2 March 5th, 2009 07:12 AM





Copyright © 2018 My Math Forum. All rights reserved.