Min + Max? #1

Algebra Level 4

{a2+b2+c2+d2=1K=ab+ac+ad+bc+bd+3cd\begin{cases} a^{ 2 }+b^{ 2 }+c^{ 2 }+d^{ 2 }=1 \\\\ K=ab+ac+ad+bc+bd+3cd \end{cases}

Let 4 real numbers aa, bb, cc, and dd satisfy the two equations above. If the minimum and maximum values of KK are mm and M,M, respectively, what is the value of m+M? m+M ?

Give your answer to 3 decimal places.

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