Funções De 2º Grau E Aplicações

Passo 1- Página 56:

1. x²- 5x + 6 ≤ 0

x²-5x+6=0

-(-5)+- √ (-5)²-4.1.6/2.1

5+-√25-24/2

5+-1/2

x'=5+1/2 x"=5-1/2

x'=6/2 x"=4/2

x'=3 x"=2

S={x E R | 2 ≤ x ≤ 3}

2. x² - 2x - 15 ≥ 0

x²-2x-15=0

-(-2)+- √ (-2)²-4.1.(-15)/2.1

2+-√4+60/2

2+-8/2

x'=2+8/2 x"=2-8/2

x'=10/2 x"=-6/2

x'=5 x"=-3

S={x E R | x ≤ -3 ou x ≥ 5}

3. x²- 4x + 4 > 0

x²-4x+4=0

-(-4)+- √ (-4)²-4.1.4/2.1

4+-√16-16/2

4+-0/2

x'=4+0/2 x"=4-0/2

x'=4/2 x"=4/2

x'=2 x"=2

S={x E R | x ≤ -3 ou x ≥ 5}

4. x²- 4x + 4 ≥ 0

x²-4x+4=0

-(-4)+- √ (-4)²-4.1.4/2.1

4+-√16-16/2

4+-0/2

x'=4+0/2 x"=4-0/2

x'=4/2 x"=4/2

x'=2 x"=2

S=R

5. x²- 4x + 4 < 0

x²-4x+4=0

-(-4)+- √ (-4)²-4.1.4/2.1

4+-√16-16/2

4+-0/2

S=Ø

6.x² - 16 >0

x² - 16 =0

x² = 16

x = +- √16

x’= 4

x”=-4

S={x E R | x < -4 ou x > 4}

7. 3x² < 9

3x²=9

x²=9/3

x=√3

x'= √3

x"= -√3

S={x E R | -√3 < x < √3}

8. x² - 3x > 2x -6

x²-3x=2x-6

x²-5x+6=0

-(-5)+- √ (-5)²-4.1.6/2.1

5 +- √25-24/2

5+-1/2

x'=5+1/2 x"=5-1/2

x'=6/2 x"=4/2

x'=3 x"=2

S={x E R | x < 2 ou x > 3}

9. x² < 2x – 1

x²=2x-1

x²-2x+1=0

-(-2)+- √ (-2)²-4.1.1/2.1

2+-√4-4/2

2+-0/2

S=Ø

10. -x² + 12x > 20

-x²+12x=20

-x²_12x-20=0

-12+-√ (12)²-4.1.20/2.(-1)

-12+-√144-80/-2

-12+-8/-2

x'=-12+8/-2 x"=-12-8/-2

x'=-4/-2 x"=-20/-2

x'= 2 x"= 10

S={x E R | 2 < x < 10}

Passo 1- Página 42:

1. 5x ≥ 20

5x = 20

x=20/5

x=4

{x ≥ 4}

2. 2x ≤ 4

2x = 4

x= 4/2

x=2

{x ≤ 2}

3. -4x ≥ 16

-4x = 16 * (-1)

4x = -16

x = -16/4

x = -4

{x ≤ -4}

4. 1/5x ≥ 3/8

1/5x = 3/8

8x = 15

x = 15/8

{x ≥ 15/8}

5.1-x/4 < 10

1-x/4 = 10

1-x = 40

-x = 39 * (-1)

x = -39

{x > -39}

6.2-x/5 ≤ 4x+1/3

2-x/5 = 4x+1/3

20x+3x=6-5

23x=1