Question

All three please 10 points

Answer 1

Answer:

A) x = 3 or -1

B) x = -7

C)x = -7

Step-by-step explanation:

A) x² + 2x + 1 = 2x² - 2

Rearranging, we have;

2x² - x² - 2x - 2 - 1 = 0

x² - 2x - 3 = 0

Using quadratic formula, we have;

x = [-(-2) ± √((-2)² - 4(1 × -3))]/(2 × 1)

x = (2 ± √16)/2

x = (2 + 4)/2 or (2 - 4)/2

x = 6/2 or -2/2

x = 3 or -1

B) ((x + 2)/3) - 2/15 = (x - 2)/5

Multiply through by 15 to get;

5(x + 2) - 2 = 3(x - 2)

5x + 10 - 2 = 3x - 6

5x - 3x = -6 - 10 + 2

2x = -14

x = -14/2

x = -7

C) log(2x + 3) = 2log x

From log derivations, 2 log x is same as log x²

Thus;

log(2x + 3) = logx²

Log will cancel out to give;

2x + 3 = x²

x² - 2x - 3 = 0

Using quadratic formula, we have;

x = [-(-2) ± √((-2)² - 4(1 × -3))]/(2 × 1)

x = (2 ± √16)/2

x = (2 + 4)/2 or (2 - 4)/2

x = 6/2 or -2/2

x = 3 or -1