Question

rozwiąż równania:

a) (x^3-5)^2-36=0

b)3x^3+5x^2-12x-20=0

c)2x^3+7x^2+7x+2=0

d)3x^3-7x^2-7x+3=0

e)4x^3-3x-1=0

f)2x^4-13x^2+6=0

g)x^4-x^2-12=0

Answer 1

a) x⁶ - 10x³ - 11 = 0

t = x³

t² - 10t - 11 = 0

Δ=100+44=144

√Δ=12

t₁ = -1

-1 = x³ x=-1

t₂ = 11

11 = x³ x=∛11

 

b) 3x³ + 5x² - 12x - 20 = 0

3x(x²-4) + 5(x²-4) = 0

(3x+5)(x-2)(x+2) = 0

x=-1⅔ ∧ x=2 ∧ x=-2

 

f) 2x⁴ - 13x² + 6 = 0

t = x²

2t² - 13t + 6 = 0

Δ=169-48=121

√Δ=11

t₁=1

x²=1 x=1 ∧ x=-1

t₂=12

x²=12 x=2√3 ∧ x=-2√3

 

g) x⁴ - x² - 12 = 0

t = x²

t²-t-12=0

Δ=49

√Δ=7

t₁=4

x=2 ∧ x=-2

t₂=-3

x² = -3 (r.sprzeczne)