# 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 $$\frac{c}{a}=53.$$

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