SOLUTION: Please help me solve sqrt(x+1)+2=sqrt(x-15)

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Question 1039581: Please help me solve
sqrt(x+1)+2=sqrt(x-15)
Found 2 solutions by solver91311, ikleyn:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!




Square both sides



Put everything but the radical term in the RHS.



*Remember this step.

Square both sides again:



Solve for x





Since you squared both sides (twice in this case), you have the potential of having introduced an extraneous root. Therefore, check the answer:







The root is extraneous and there was only one root, so the solution set is the empty set. Now, look back at the step I pointed out to remember. 4 is a positive number and is a positive number because an unsigned even-indexed radical is defined as the positive root. Since a positive number multiplied by a positive number is positive, such a product cannot be equal to a negative number, specifically -20. Therefore, we could have quit at this step because it is clear that the equation has no solution.

John

My calculator said it, I believe it, that settles it
Answer by ikleyn(52795)   (Show Source): You can put this solution on YOUR website!
.
Please help me solve
sqrt(x+1)+2=sqrt(x-15)
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