Question

Polinomul x^3 -2x^2+1 cu rădăcinile X1,X2,X3 . Calculați X1 1 + X2 2 +X3 2

Answer 1

X³ - 2X² + 1 = 0
a = 1
b = -2
c = 0
d = 1
----------------------------
x₁ + x₂ + x₃ = -b / a = -(-2) / 1 = 2
x₁x₂ + x₁x₃ + x₂x₃ = c / a = 0 / 1 = 0
x₁x₂x₃ = -d / a = -1

Pentru a afla x₁² + x²₂ + x₃² ridicam prima expresie la patrat.
x₁ + x₂ + x₃ = 2 | ()²
x₁² + x²₂ + x₃² + 2x₁x₂ + 2x₁x₃ + 2x₂x₃ = 4
x₁² + x²₂ + x₃² + 2 (x₁x₂ + x₁x₃ + x₂x₃) = 4
x₁² + x²₂ + x₃² + 2·0 = 4
x₁² + x²₂ + x₃² = 4