Question

Rozwiąż równanie:
a)
b)
c)

Z góry dziękuję za pomoc ;)

Answer 1

a)

3x^4-6x^3-12x^2=0

3x^2(x^2-2x-4)=0

3x^2=0        Δ=20

x=0            x1=1-

                 x2=1+

 

b)

10x^5+15x^3=5x^4

10x^5-5x^4+15x^3=0

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

5x^3=0        Δ<0

 

c)

x^3+2x^2=5x+10

x^3+2x^2-5x-10=0

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

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

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

x=

x=-

x=-2

 

Answer 2

a)

3x⁴-6x³-12x² = 0

3x²(x²-2x-4) = 0

3x² = 0   => x = 0

lub

x²-2x-4 = 0

Δ = b²-4ac = 4+16 = 20

√Δ = √20 = 2√5 

x1 = (-b-√Δ)/2a = (2-2√5)/2 = 1-√5

x2 = (-b+√Δ)/2a = (2+2√5)/2 = 1+√5

Odp. x = 1-√5   v   x = 0   x = 1+√5

 

b)

10x⁵+15x³ = 5x⁴

10x⁵-5x⁴+15x³ = 0  /:5

2x⁵-x⁴+3x³ = 0

x³(2x²-x+3) = 0

x³ = 0   => x = 0

lub

2x²-x+3 = 0

Δ = 1-24 = -23

Δ < 0, brak pierwiastków równania

Odp. x = 0

 

c)

x³+2x² = 5x+10

x³+2x²-5x-10 = 0

x²(x+2)-5(x+2) = 0

(x+2)(x²-5) = 0

(x+2)(x+√5)(x-√5) = 0

x+2 = 0   => x = -2

lub

x+√5 = 0   => x = -√5

lub

x-√5 = 0   => x = √5

Odp. x = -√5   v   x = -2   v   x = -√5