Question

Which statement about √2x+3 = √√2x + 3 is true?

O
O
1
is an extraneous solution.
x=3/21 is a true solution.
Ox=2 is an extraneous solution.
Ox=2 is a true solution.

Answer 1

The statement x=2 is an extraneous solution.

Step-by-step explanation:

The statement √2x+3 = √√2x + 3 is true if x=2. Let's solve the equation step by step to determine whether x=2 is the only solution or if there are any extraneous solutions. Start by squaring both sides of the equation to remove the square root: 2x+3 = √2x + 3. Then, square both sides again to remove the square root: 4x^2 + 12x + 9 = 2x + 3. Simplify and rearrange the equation to get 4x^2 + 10x + 6 = 0. By using the quadratic formula, we find that x = -3/2 or x = -1/2. Since none of these solutions satisfy the original equation, the statement x=2 is an extraneous solution.

Learn more about Extraneous solutions