Question

Urgente!
Resolver as equações abaixo:

| x – 1 | = 5

| x + 1 | = | 2x – 3 |

| 2x + 1 | = 5x – 2

| x |² - 2 |x | - 3 = 0

Answer 1

Resposta:

| x – 1 | = 5

|x-1|=5

x=5-1

x=4

| x + 1 | = | 2x – 3 |

x+2x=-3+1

3x=-2

x=-2/3

| 2x + 1 | = 5x – 2

2x-5x=-2+1

-3x=-1 (-1)

x=1/3

| x |² - 2 |x | - 3 = 0

x^2+2x-3=0

$x = \frac{ - (2) + - \sqrt{( {2)}^{2} - 4 \times 1 \times ( - 3) } }{2 \times 1} = \frac{ - 2 + - \sqrt{4 + 12} }{2} = \frac{ - 2 + - \sqrt{16} }{2} = \\ \\ x1 = \frac{ - 2 + \sqrt{16} }{2} = \frac{ - 2 + 4}{2} = \frac{2}{2} = 1 \\ x2 = \frac{ - 2 - \sqrt{16} }{2} = \frac{ - 2 - 4}{2} = \frac{ - 6}{2} = - 3$

espero que isso ajude vc

Answer 2

Oie, Td Bom?!

1.

|x - 1| = 5

• x - 1 = 5

x = 5 + 1

x₂ = 6

• x - 1 = - 5

x = - 5 + 1

x₁ = - 4

S = {- 4 , 6}

2.

|x + 1| = |2x - 3|

• x + 1 = 2x - 3

x - 2x = - 3 - 1

- x = - 4 . (- 1)

x₂ = 4

• x + 1 = - (2x - 3)

x + 1 = - 2x + 3

x + 2x = 3 - 1

3x = 2

x₁ = 2/3

S = {2/3 , 4}

3.

|2x + 1| = 5x - 2

|2x + 1| - 5x = - 2

• 2x + 1 - 5x = - 2 , 2x + 1 ≥ 0

- 3x + 1 = - 2 , 2x ≥ - 1

- 3x = - 2 - 1 , x ≥ - 1/2

- 3x = - 3

x = -3/-3

x = 3/3

x = 1

• - (2x + 1) - 5x = - 2 , 2x + 1 < 0

- 2x - 1 - 5x = - 2 , 2x < - 1

- 7x - 1 = - 2 , x < - 1/2

- 7x = - 2 + 1

- 7x = - 1

x = -1/-7

x = 1/7

x = 1 , x ≥ - 1/2 ⇒ x = 1

x = 1/7 , x < - 1/2 ⇒ x∈∅

S = {1}

4.

|x|² - 2 . |x| - 3 = 0

x² - 2 . |x| - 3 = 0

• x² - 2x - 3 = 0 , x ≥ 0

x² + x - 3x - 3 = 0

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

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

x + 1 = 0 ⟹ x₁ = - 1

x - 3 = 0 ⟹ x₂ = 3

• x² - 2 . (- x) - 3 = 0 , x < 0

x² + 2x - 3 = 0

x² + 3x - x - 3 = 0

x . (x + 3) - (x + 3) = 0

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

x + 3 = 0 ⟹ x₁ = - 3

x - 1 = 0 ⟹ x₂ = 1

x₁ = - 1 , x ≥ 0 ⇒ x = 3

x₂ = 3

x₁ = - 3 , x < 0 ⇒ x = - 3

x₂ = 1

S = {- 3 , 3}

Att. Makaveli1996