Question

Wyznacz r.

-8r³ + 8Rr² - R³ = 0

Answer 1

 -8 r³ + 8Rr² - R³ = 0

 -8 r³ + 4Rr² + 4Rr² - R³ = 0

- 4r² (2r - R) + R (4r² - R²) = 0

- 4r² (2r - R) + R (2r - R)(2r + R) = 0

 (2r - R) ( -4r² + 2Rr + R²) =0

 2r - R = 0           Δ= 4R² - 4 · (-4) ·R² = 4R² + 16R² = 20R²    √Δ = 2√5R

  2r = R /:2                 r₂ = (-2R -2√5R)/(-8) = (2R + 2√5R)/8

  r₁ = R/2                   r₃ = (2R - 2√5R)/8