Mathcounts National Sprint Round Problems And Solutions Direct

Line AE: from A(0,0) to E(3,15): slope = 15/3=5, equation y=5x. Line BD: from B(8,0) to D(0,15): slope = (15-0)/(0-8) = -15/8, equation: y = (-15/8)(x-8) = (-15/8)x + 15.

Then (x^3 + y^3 = (x+y)(x^2 - xy + y^2) = 8 \cdot (34 - 15) = 8 \cdot 19 = 152). Mathcounts National Sprint Round Problems And Solutions

(\boxed152)

Let’s solve correctly: (17(a+b)=3ab) → (3ab - 17a - 17b = 0) → Add (289/3)? No, use Simon’s favorite: Multiply by 3: (9ab - 51a - 51b = 0) → Add 289: ((3a-17)(3b-17) = 289). Yes! Because ((3a-17)(3b-17) = 9ab - 51a - 51b + 289 = 289). Line AE: from A(0,0) to E(3,15): slope =

Thus min sum = 108.