City Zhautykov 2025 Grade 8 Problem 8
Solve the system of equations in reals $$\left\{ \begin{matrix} 2\sqrt{a}=b^{2025}+c^{2025},\\ 2\sqrt{b}=a^{2025}+c^{2025}, \\ 2\sqrt{c}=a^{2025}+b^{2025}. \end{matrix}\right.$$
import Mathlib.Data.Real.Sqrt
def answer : Set (ℝ × ℝ × ℝ) := sorry
theorem solution (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) :
2 * √a = b ^ 2025 + c ^ 2025 ∧
2 * √b = a ^ 2025 + c ^ 2025 ∧
2 * √c = a ^ 2025 + b ^ 2025 ↔
(a, b, c) ∈ answer := sorry
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