x² - 3x - 2 = 0
По теореме Виета :
x₁ * x₂ = - 2
x₁ + x₂ = 3
x₁ * x₂³ + x₁³ * x₂ = x₁x₂ * (x₂² + x₁²) = x₁x₂ * [(x₁ + x₂)² - 2x₁x₂] = - 2 * [3² - 2 * (- 2)] =
= - 2 * (9 + 4) = - 2 * 13 = - 26
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Verified answer
x² - 3x - 2 = 0
По теореме Виета :
x₁ * x₂ = - 2
x₁ + x₂ = 3
x₁ * x₂³ + x₁³ * x₂ = x₁x₂ * (x₂² + x₁²) = x₁x₂ * [(x₁ + x₂)² - 2x₁x₂] = - 2 * [3² - 2 * (- 2)] =
= - 2 * (9 + 4) = - 2 * 13 = - 26
Д=9+8=17>0
по теорема Виеета
х1+х2=3
х1*х2=-2
х1х2³+х1³*х2=х1•х2(х2²+х1²)=
-2(х1²+2х1х2+х2²-2х1х2)=
-2*(х1+х2)²+4х1х2=-2•3²+4(-2)=
=-18-8=-26