City Zhautykov 2024 Grade 8 Problem 1

Reals $a, b$ satisfy $a + b = ab = 19$. Find the value of $$(a^2-19a)\left(b+\frac{19}{b}\right).$$

Replace sorry in the template below with your solution. See Answer Bank for acceptible answer declarations. Mathlib version used by the checker is v4.34.0.

import Mathlib.Data.Real.Basic

def answer : ℝ := sorry

theorem solution (a b : ℝ) (h1 : a + b = 19) (h2 : a * b = 19) :
    (a ^ 2 - 19 * a) * (b + 19 / b) = answer := sorry

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