# Is it Symmetric?

**Algebra**Level 5

*Let* \(x_{1} , x_{2} , x_{3} ,x_{4}\) *be real numbers such that*

\(\frac{1}{2}\leq x_{1}^{2} + x_{2}^{2} + x_{3}^{2} + x_{4}^{2} + x_{5}^{2} \leq 1\)

\(A = (x_{1} - 2x_{2} + x_{3})^{2} + (x_{2} - 2x_{3} + x_{1})^{2} + (x_{2} - 2x_{1})^{2} + ( - 2x_{4} + x_{3})^{2}\)

\( A \in [ \frac{a -b\sqrt{c}}{d} , \frac{e + f\sqrt{g}}{h}]\)

*Find* \(a + b + ........... + h\)

*Note - It contains the favourite number of Sandeep Bhardwaj and Sanjeet Raria , when A is maximum*