Question

What are the real solutions to the equation:

|x|²+2|x|-3=0?


F) 1,-1
G) 3,-3
H) 1,3
J) -1,-3
K)1,-1,3,-3

Answer 1

F) 1, -1

Explanation:

You want the real solutions to |x|² +2|x| -3 = 0.

Solution

We can let z = |x|. Then the equation becomes ...

z² +2z -3 = 0

(z +3)(z -1) = 0 . . . . . factored

The solutions will be the values of z that make the factors zero:

z +3 = 0 ⇒ z = -3

z -1 = 0 ⇒ z = 1

Z = -3

Substituting our definition of z, we have ...

|x| = -3

The absolute value is never negative, so there are no values of x that satisfy this equation.

Z = 1

Substituting our definition of z, this is ...

|x| = 1

This is true for x = ±1.

The real solutions to the equation are 1, -1.