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Below is a few practice problems of various difficulty, but you will need considerably more practice than one each. For that reason
you should definitely use the green “Try Another” button in the top right corner at least two or three times to complete
additional versions of these questions for more practice. You should keep using that button until doing these problems feels straight
forward and easy, and then come back after a week or so of doing other stuff and try again to make sure it is still just as easy for
you.
Theoretically Easier Difficulty Problem
Start by squaring both sides.
Solve for as normal.
Remember to check your solutions to see if they work - it is possible to do everything correct, and still get a bad answer - known
as an “extraneous solution”.
What is the real-valued solutions to the following equality? (If there is no answer, enter DNE). .
Theoretically Medium Difficulty Problem
Start by squaring both sides.
Solve for as normal.
Remember to check your solutions to see if they work - it is possible to do everything correct, and still get a bad answer - known
as an “extraneous solution”.
What is the sum of the real-valued solutions to the following equality? (If there are no solutions, enter DNE)
.
Theoretically Harder Difficulty Problem
Start by isolating one of the square roots and then squaring both sides.
Remember to expand out both sides correctly. For the side you isolated a square root, squaring that side should simply remove
the square root. For the other side, you may need to expand out the square by using distribution.
Once you have expanded out everything, isolate the remaining square root (if there is one) and square both sides again to get rid
of the last square root.
Once no more square roots remain, solve for as normal.
Remember to check your solutions to see if they work - it is possible to do everything correct, and still get a bad answer - known
as an “extraneous solution”.
What is the sum of the real-valued solutions to the following equality? If there are no solutions, enter DNE) The sum of solutions
is: .
