lean_workbook_plus_60997

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Solve the following system of equations on $\mathbb{R}^3$ \n $x^2+y^2+z^2=1$ \n $x+y+2z=\sqrt7$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_60997 (x y z : ℝ) (h₁ : x^2 + y^2 + z^2 = 1) (h₂ : x + y + 2*z = Real.sqrt 7) : x = 2/3 ∧ y = 2/3 ∧ z = 1/3   :=  by sorry

Source