a, b, c, d ∈ R

and ad-bc=1

find the minimum of a^{2}+b^{2}+c^{2}+ac+bd

help me!! thanks :)

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- March 21st 2013, 09:40 AMli00512Help!! find the minimum
a, b, c, d ∈ R

and ad-bc=1

find the minimum of a^{2}+b^{2}+c^{2}+ac+bd

help me!! thanks :)

- March 22nd 2013, 04:22 AMchiroRe: Help!! find the minimum
Hey li00512.

Have you been taught multivariable calculus and Lagrange multipliers? There may be a simpler solution, but this a systematic approach for optimization problems. - March 22nd 2013, 04:33 AMli00512Re: Help!! find the minimum
hi, chiro.

I want to find a simpler way to solve this problem.

and I just realized that I mistyped the problem.

sorry, it should be "find the minimum of a2+b2+c2+d2+ac+bd".