Solving D S.'s system of equation

Algebra Level 5

For all pairs of nonzero real numbers (x,y)(x,y) such that 24x310x2y3xy2+y3=024x^3 - 10x^2y - 3xy^2 + y^3 = 0 and x2+5x=y2x^2 + 5x = y^2, let (a,b)(a,b) denote the solution with the largest value of xx. What is the value of a+ba + b?

This problem is posed by D S.

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