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fahad nasir November 18th, 2018 09:00 AM

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?

romsek November 18th, 2018 11:20 AM

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.


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