Question

Solve for x in the equation x² = 5. Is the solution extraneous?

a. x= √5, solution is not extraneous
b. x=−√5, solution is extraneous
c. x= √3, solution is not extraneous
d. x=−√3, solution is extraneous

Answer 1

The solutions to the equation x² = 5 are x = √5 and x = -√5, and neither of them is extraneous. They are valid solutions since both when squared result in 5.

Step-by-step explanation:

To solve for x in the equation x² = 5, we need to find all possible values of x that when squared, equal 5. There are two solutions:

1. x can be the positive square root of 5: x = √5.
2. x can also be the negative square root of 5: x = -√5.

Since squaring either the positive or negative square root of 5 will yield the original equation x² = 5, neither solution is extraneous. They are both valid solutions to the equation. Therefore, the answers a and b are correct and not extraneous, whereas answers c and d are incorrect since they do not pertain to our original equation.