Maximize an Almost-Factorable Expression
Algebra
Level
5
Real numbers \(a,b,c,d\) satisfy
\[a^2+b^2=c^2+d^2.\]
If the maximum of the expression
\[\dfrac{20bc+14bd+20ad-14ac}{a^2+b^2+c^2+d^2}\]
can be expressed as \(\sqrt{n}\) for some positive integer \(n\), what is the value of \(n?\)
by
Daniel Liu