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Algebra Level 5

If a,bRa,b\in \mathbb{R} such that E=(ab)2+(2ab)2+(2a3b)2 E=\sqrt { { (a-b) }^{ 2 }+ (2-a-b )^{ 2 }+{ (2a-3b) }^{ 2 } } And If minimum value of EE can be expressed as Emin=mn { E }_{ min }=\frac { m }{ \sqrt { n } } where m,nm,n are integers such that nn is a square free integer, then find the value of m+n\displaystyle \mathrm{m + n}.

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