My name is Merin and I am a student. I am in my last year of high school but am taking a grade 11 pure math course.
I am quite confused about solving radical equations. This is what I understand:
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V x-3 = 3
Then you would square each side to get ride of the radical sign and then you solve the problem from there. (x=12 right?)
However, what about a problem with two radicals? For example:
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V x-2 + V 3x-3 = 3
No matter what I try I cant get the right answer!! Please help!!!
Merin
Hi Marin,
I'm going to write sqrt for the square root.
First rewrite sqrt(x-2) + sqrt(3x-3) = 3 with one of the roots isolated on the left side of the equation
sqrt(x - 2) + sqrt(3x - 3) = 3
sqrt(x - 2) = 3 - sqrt(3x - 3)
Now square both sides
[sqrt(x - 2)]2 = [3 - sqrt(3x - 3)]2
x - 2 = 9 - 6 sqrt(3x - 3) + (3x - 3)
Simplify to isolate the square root term on the left of the equation
x - 2 = 9 - 6 sqrt(3x - 3) + (3x - 3)
6 sqrt(3x - 3) = 2x + 8
3 sqrt(3x - 3) = x + 4
Now you are in the situation of one radical which you can solve by again squaring both sides.
In these problems it is especially important that you verify the answer that you find. The process of squaring will, at times, introduce a solution to the final equation that is not a solution of the initial equation.
Penny