Four Equations, Four Unknowns (Differential Equation?)

[HenryHattendorf]

Hi,

I'm a bit rusty with my optimization. Not sure if I need Lagrangian to solve this or matrix notation? I have no experience w/ differential equations, but perhaps that would be the best way to go? Any help would be appreciated.

I have four equations and four unknowns (w₁, w₂, x₁, and x₂):


w₁ + w₂ = pi/2
w₁x₁ + w₂x₂ = pi²/8
w₁x_1² + w₂x₂² = pi³/12
w₁x₁³ + w₂x₂³ = pi⁴/64

Thanks