How do you solve #sqrt(4a + 1) = 1 # and find any extraneous solutions?

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Answer 1 · 2017-03-29T03:28:53

Square both sides.
Solve the resulting equation.
Check the solution.

Given: #sqrt(4a + 1) = 1#

Square both sides:

#4a + 1 = 1#

Subtract 1 from both sides:

#4a = 0#

Divide both sides by 4:

#a = 0#

Check the solution:

#sqrt(4(0) + 1) = 1#

#1 = 1#

This checks.

There is 1 and only 1 solution and it checks, therefore, there are no extraneous solutions.