Min + Max? #1

Algebra Level 4

\[\begin{cases} a^{ 2 }+b^{ 2 }+c^{ 2 }+d^{ 2 }=1 \\\\ K=ab+ac+ad+bc+bd+3cd \end{cases} \]

Let 4 real numbers \(a\), \(b\), \(c\), and \(d\) satisfy the two equations above. If the minimum and maximum values of \(K\) are \(m\) and \(M,\) respectively, what is the value of \( m+M ? \)

Give your answer to 3 decimal places.

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