Question

Zad. Rozwiąż równania i nierówności.

Answer 1

a)

x²+8x-16=0

Δ=8²-4*1*(-16)
Δ=64+64

Δ=128

√Δ=8√2

 

x₁=(-8-8√2)/(2*1)

x₁=-4-4√2

 

x₂=(-8+8√2)/(2*1)

x₂=-4+4√2

 

b)

6x²=-5x

6x²+5x=0

x(6x+5)=0

x=0

 

6x+5=0

6x=-5

x=-5/6

 

c)

5x-3=2x²

2x²-5x+3=0

2x²-2x-3x+3=0

2x(x-1)-3(x-1)=0

(2x-3)(x-1)=0

2x-3=0

2x=3

x=3/2 ∨ x=1

Answer 2

a) x²+8x-16=0

a=1

b=8

c=-16

Δ=b²-4ac

Δ=8²-4*1*(-16)=64+64=128

Δ=128

√Δ=8√2

x₁=-b-√Δ:2a=-8-8√2:2*1=-8-8√2:2=-4-4√2

x₂=-b+√Δ:2a=-8+8√2:2*1=-8+8√2:2=-4+4√2

 

b)6x²=-5x

6x²+5x=0

x(6x+5)=0

x=0 lub

6x+5=0

6x=-5 /:6

x=-5/6

 

c)5x-3=2x²

-2x²+5x-3=0

a=-2

b=5

c=-3

Δ=b²-4ac

Δ=5²-4*(-2)*(-3)=25-24=1

Δ=1

√Δ=1

x₁=-b-√Δ:2a=-5-1:2*(-2)=-6:(-4)=1,5

x₂=-b+√Δ:2a=-5+1:2*(-2)=-4:(-4)=1