Solve the equation. Identify any extraneous solutions. √a=-2
A.4 is a solution of the original equation.
B.4 is a solution of the original equation. -4 is an extraneous solution*****
C.-4 is a solution of the original equation. -4 is an extraneous solution
D.No solution
I messed up on these before, can someone walk me through the steps?
√a means the positive square root of a
√4 = 2, not ±2
Just because (-2)^2 = 4 does not make -2 equal to √4
So, as written, the equation has no solution, because √4 = 2, not -2
Ohhh... Now I see it.
Thanks! :)
To solve the equation √a = -2, we have to isolate the variable 'a'.
Step 1: Square both sides of the equation to eliminate the square root.
(√a)^2 = (-2)^2
a = 4
So, we find that a = 4 is a solution of the original equation.
However, when we substitute a = 4 back into the original equation, we get:
√4 = -2
The square root of 4 is 2, not -2.
So, a = 4 is an extraneous solution to the original equation.
Hence, the correct answer is B. 4 is a solution of the original equation, and -4 is an extraneous solution.
To solve the equation √a = -2, we first need to square both sides of the equation to eliminate the square root symbol. Squaring both sides gives us a = (-2)^2 = 4.
Next, we need to check if the solution 4 satisfies the original equation. Substituting a = 4 into the original equation √a = -2, we get √4 = -2. The square root of 4 is 2, so this equation becomes 2 = -2, which is not true.
Since 4 is not a solution of the original equation, we can conclude that there are no valid solutions. Therefore, the correct answer is option D: No solution.
Extraneous solutions are solutions that appear to satisfy the equation but actually do not. In this case, there are no extraneous solutions because there are no valid solutions to begin with.