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2010-02-13T19:23:45+01:00
A)

x⁶ = (x³)² = t²

t² + 25t - 54 = 0

Δ = b² - 4ac
Δ = 25² - 4 × 1 × (-54)
Δ = 625 + 216
Δ = 841
Δ = √841
√Δ = 29

t₁ = (-25 - 29)/2 = -54/2 = -27
t₂ = (-25 + 29)/2 = 4/2 = 2
t = x³
x³ = -27
x = - 3
albo
x³ = 2
x = ∛2

b)

3t² + 4t + 1 = 0

Δ = 16 - 12 = 4
√Δ = 2
t₁ = (-4 - 2)/6 = -1
t₂ = (-4 + 2)/6 = -⅓

x³ = -1
x = -1
albo
x³ = -⅓
x = ∛9/3