Long one

Algebra Level 5

Solve the given equations :\[31x^2y^2-7y^4-112xy+64=0\] \[ x^2-7xy+4y^2+8=0\]

The solutions of \(x\) and \(y\) are in the below given forms :

\(x=y=\pm A\)

\(x=-y=\pm i \sqrt{\frac{B}{C}}\)

\(x=\pm D,\) \(y=\pm E\)

\(x=\pm i \sqrt{\frac{F}{G}},\) \(y=\mp i \sqrt{\frac{H}{I}}\)

Find \(A+B+C+D+E+F+G+H+I\).

Details :

\(i=\sqrt{-1}\)

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