An algebra problem by Achal Jain

Algebra Level pending

Let \(a,b,c,d\) be positive real numbers such that \(a+b+c+d=4\).

What is the minimum value of

\[ \frac { 1 }{ { a }^{ 2 }+1 } +\frac { 1 }{ { b }^{ 2 }+1 } +\frac { 1 }{ { c }^{ 2 }+1 } + \frac { 1 }{ { d }^{ 2 }+1 } ?\]

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