Question

What are the real solutions to the equation: |x|² - 2|x| - 3 = 0?

A) x = -1, x = 3
B) x = -1, x = -3
C) x = 1, x = 3
D) x = 1, x = -3

Answer 1

The solutions to the equation |x|² - 2|x| - 3 = 0 are x = 3 and x = -1.

Step-by-step explanation:

To solve the equation |x|² - 2|x| - 3 = 0, we can rewrite it as a quadratic equation by substituting |x| as a variable:

x² - 2x - 3 = 0

Now, we can solve this quadratic equation using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 1, b = -2, and c = -3. Substituting these values into the formula, we have:

x = (-(-2) ± √((-2)^2 - 4(1)(-3))) / (2(1))

Simplifying further,

x = (2 ± √(4 + 12)) / 2

x = (2 ± √16) / 2

x = (2 ± 4) / 2

Finally, we get two solutions:

x = 3

x = -1