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 Algebra Pre-Algebra and Basic Algebra Math Forum

 November 18th, 2018, 09:00 AM #1 Member   Joined: Oct 2012 Posts: 78 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? November 18th, 2018, 11:20 AM #2 Senior Member   Joined: Sep 2015 From: USA Posts: 2,552 Thanks: 1402 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 11:30 AM. Tags minimum Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post 3uler Calculus 3 November 23rd, 2014 07:08 AM Monox D. I-Fly Pre-Calculus 4 October 13th, 2014 05:58 AM proglote Algebra 13 April 29th, 2011 05:46 PM ely_en Algebra 9 October 25th, 2009 05:59 PM K Sengupta Number Theory 2 March 5th, 2009 06:12 AM

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