SOLUTION: What is the root of 2-2sqrt( 3x )=1-sqrt( 3x )

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Question 668283: What is the root of 2-2sqrt( 3x )=1-sqrt( 3x )
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The easy part:
2-2sqrt%28+3x+%29=1-sqrt%28+3x+%29 <--> 2-2sqrt%28+3x+%29%2B2sqrt%28+3x+%29=1-sqrt%28+3x+%29%2B2sqrt%28+3x+%29 <--> 2=1%2Bsqrt%28+3x+%29 <--> 2-1=1%2Bsqrt%28+3x+%29-1 <--> 1=sqrt%28+3x+%29
Next:
1=sqrt%28+3x+%29 --> 1%5E2=%28sqrt%28+3x+%29%29%5E2 --> 1=3x <--> x=1%2F3

The very necessary verification:
2-2sqrt%28+3%2A%281%2F3%29+%29=2-2sqrt%28+1%29=2-1=0 and
1-sqrt%28+3%2A%281%2F3%29%29=1-sqrt%281%29=1-1=0
Since x=1%2F3 verifies that 2-2sqrt%28+3x+%29=1-sqrt%28+3x+%29,
highlight%28x=1%2F3%29 is the solution.

NOTE that some arrows go in one direction only.
When we square both sides, we may be introducing new solutions.
That is why we need to verify that each solution of the equations after squaring is a solution of the original equation.