Question

Rozwiąż

a)(1-2x)kwadrat = 2x -xkwadrat +1

b) 3x kwadrat - x -2=0

c) 4xkwadrat=1

Answer 1

a)

(1-2x)² = 2x-x²+1

1-4x+4x² = 2x-x²+1

4x²-4x = -x²+2x

4x²+x² = 2x+4x

5x² = 6x

5x²-6x = 0

Δ = (-6)²-4*5*0

Δ = 36

√Δ = 6

x1 = (6-6)/10

x1 = 0

x2 = (6+6)/10

x2 = 1,2

 

b)

3x²-x-2 = 0

Δ = (-1)²-4*3*(-2)

Δ = 1+24

Δ = 25

√Δ = 5

x1 = (1-5)/(2*3)

x1 = -4/6

x1 = -2/3

x2 = (1+5)/(2*3)

x2 = 6/6

x2 = 1

 

c)

4x² = 1 |:4

x² = 1/4

x = 1/2 lub -1/2