Question

Rozwiąż równania
a) 2(x-1)+x=x-3(2-3x)
b) 2x²-10x-12=0
c) 3x³+3x²-12x-12=0

Answer 1

A)

2(x-1)+x=x-3(2-3x)
2x - 2 + x = x - 6 + 9x
2x + x - x -9x = 2 - 6
7x = 4 |:7
x = (4/7)

b) (równanie kwadratowe więc wyliczamy: Δ, x₁ i x₂)

2x²-10x-12=0

a = 2
b = -10
c = -12

Δ = b² - 4ac
Δ = 100 - 4 * 2 * -12
Δ = 100 + 96 (minus razy minus daje+)
Δ = 196
√Δ = 14

x₁ = -b - √Δ / 2a = 10 - 14 / 4 = -4/4 = -1
x₂ = -b + √Δ / 2a = 10 + 14 / 4 = 24/4 = 6

c)

3x³ + 3x² - 12x - 12 = 0
3x² * ( x + 1 ) - 12 * ( x + 1 ) = 0
( 3x² - 12 ) * ( x + 1 ) = 0
3 * ( x² - 4 ) * ( x + 1 ) = 0
3 *( x - 2 ) * ( x + 2 ) * ( x + 1 ) = 0
x₁ = -2
x₂ = -1
x₃ = 2

licze na naj ;)

Answer 2

A) 2(x-1)+x=x-3(2-3x)
2x - 2 + x = x - 6 + 9x
3x - x -9x = - 6 + 2
-7x = -4 |:(-7)
x = 4/7

b)2x²-10x-12=0
Δ = b² - 4ac
Δ = (-10)² - 4 * 2 * (-12)
Δ = 100 + 96
Δ = 196
√Δ =√196
√Δ = 14

x₁ = 10 - 14 / 4 = -4/4 = -1
x₂ = 10 + 14 / 4 = 24/4 = 6

c) 3x³ + 3x² - 12x - 12 = 0
3x²( x + 1 ) - 12( x + 1 ) = 0
( 3x² - 12 )( x + 1 ) = 0
3 ( x² - 4 ) * ( x + 1 ) = 0
3( x - 2 )( x + 2 )( x + 1 ) = 0
x₁ = 2 x₂ = -2 x₃ = -1