The End of Faith in Quadratics

Algebra Level 5

If the minimum value of the quadratic expression \(ax^2+bx+c\) with real coefficients is 6 then find the sum of minimum and maximum values of the expression \[S=\frac{x^2+y^2}{ay^2+bxy+cx^2}\] when \(\frac{c}{a}=53.\)

Note: This is my original problem. For more of my problems check the set Questions I've Made

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