Question

rozwiaz rownania

4x2-20x+9=0

(2x-1)*(x+2)=3

4x2+5x=1<0

5(2x-1)(x+4)<0

x3-4x2+3x=0

x3-2x2-x+2=0

x3+2x2-2x-4=0

Answer 1

4x²-20x+9=0

Δ=20²-4*4*9 =400-144 =256

√Δ = 16

 

x₁=(20-16)/(2*4)= 4/8 = 1/2

x²=(20+16)/(2*4)= 36/8 = 4 i 1/2

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(2x-1)*(x+2)=3

2x²+4x-x-2-3=0

2x²+3x-5=0

Δ=3²-4*2*(-5) = 9+40=49

√Δ = 7

 

x₁=(-3-7)/(2*2)= -10/4 = -2 i 1/2

x²=(-3+7)/(2*2)= -4/4 = -1

 

--------------------------

4x²+5x+1<0 *

Δ=5²-4*4*1

Δ=25-16

Δ=9

√Δ = 3

 

x₁=(-5-3)/(2*4)= -8/8 = -1

x²=(-5+3)/(2*4)= -2/8 = -1/4

 

a>0 zatem rysujemy parabole ramionami skierowanymi do góry... zatem wartości mniejsze od zera będą w przedziale (-1/4; -1)

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5(2x-1)(x+4)<0

5*[2x²+8x-x-4]<0

10x²+35x-20<0 /:5

2x²+7x-4 <0

Δ=7²-4*2*(-4) = 49+32=81

√Δ = 9

 

x₁=(-7-9)/(2*2)= -16/4 = -4

x²=(-7+9)/(2*2)= 2/4 = 1/2

a>0 ramiona do góry x należy od (-4;1/2)

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x3-4x²+3x=0

x^3-4x²+3x=0

x(x²-4x+3)=0

wyciągam równanie kwadratowe i licze miejsca zerowe

Δ=4²-4*3 = 16-12=4

√Δ = 2

 

x₁=(4-2)/2= 2/2 = 1

x²=(4+2)/2= 6/2 = 3

Zatem:

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

x=0

x=1

x=3

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x3-2x²-x+2=0

x^3-x-2x²+2=0

x(x²-1) -2 (x²-1)=0

(x²-1)(x-2)=0

x²=1 / √

|x|=1

x=1 lub x=-1

oraz

x=2

-------------------------

x3+2x²-2x-4=0

x²(x+2)-2(x+2)=0

(x²-2)(x+2)=0

x=-2

oraz

x²-2=0

x²=2 /√

|x|=√2

x=√2 lub x=-√2

 

 

*Zakładam, że zamiast "=" miało być "+"

Answer 2

1 . 4x²-20x+9=0

Δ=20²-4*4*9 =400-144 =256

√Δ = √16 = 4

 

x₁=(20- 4)/(2*4)= 16/8 = 2

x²=(20+ 4)/(2*4)= 24/8 = 3

 

 

2 . (2x-1)*(x+2)=3

2x²+4x-x-2-3=0

2x²+3x-5=0

Δ=3²-4*2*(-5) = 9+40=49

√Δ = 7

 

x₁=(-3-7)/(2*2)= -10/4 = -2 i 1/2

x²=(-3+7)/(2*2)= -4/4 = -1

 

3. 4x²+5x+1<0 *

Δ=5²-4*4*1

Δ=25-16

Δ=9

√Δ = 3

 

x₁=(-5-3)/(2*4)= -8/8 = -1

x²=(-5+3)/(2*4)= -2/8 = -1/4

 

 

4. 5(2x-1)(x+4)<0

5*[2x²+8x-x-4]<0

10x²+35x-20<0 /:5

2x²+7x-4 <0

Δ=7²-4*2*(-4) = 49+32=81

√Δ =√ 9 = 3

 

x₁=(-7-3)/(2*2)= -10/4 = - 2 i 1/4

x²=(-7+3)/(2*2)= 4/4 = 1

 

5 . x3-4x²+3x=0

x^3-4x²+3x=0

x(x²-4x+3)=0

 

Δ=4²-4*3 = 16-12=4

√Δ = 2

 

x₁=(4-2)/2= 2/2 = 1

x²=(4+2)/2= 6/2 = 3

 

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

x=0

x=1

x=3

 

6 . x3-2x²-x+2=0

x^3-x-2x²+2=0

x(x²-1) -2 (x²-1)=0

(x²-1)(x-2)=0

x²=1 / √

|x|=1

x=1 lub x=-1

oraz

x=2

 

7 . x3+2x²-2x-4=0

x²(x+2)-2(x+2)=0

(x²-2)(x+2)=0

x=-2

 

x²-2=0

x²=2 /√

|x|=√2

x=√2 lub x=-√2