SOLUTION: 2 Square root (m-1) - Sqaure root(3m-1)=0 which means: 2 )m-1 - )3m-1=0 replace closed parenthesis with root symbol

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Question 350041: 2 Square root (m-1) - Sqaure root(3m-1)=0
which means: 2 )m-1 - )3m-1=0

replace closed parenthesis with root symbol
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
2 Square root (m-1) - Sqaure root(3m-1)=0
is clear while
which means: 2 )m-1 - )3m-1=0
is unintelligible.

2sqrt%28m-1%29+-+sqrt%283m-1%29=0
To solve equations where the variable is inside one or more square roots
  1. Isolate a square root.
  2. Square both sides of the equation.
  3. If there are still any square roots left, repeat steps #1 and #2.
  4. At this point you should have an equation without square roots. Solve thie equation using techniques appropriate for the type of equation it is.
  5. Check your answer(s)! This is more than just a good idea. Whenever you square both sides of an equation (like we have done at least once at step #2), you may introduce what are called "extraneous solutions". Extraneous solutions are solutions which work in the squared equation but not in the original equation. Extraneous solutions can occur even if no mistakes are made. So we must check all possible solutions and make sure they work in the original equation. If not, then we must reject the solution.

Let's see how this works on your equation:
1) Isolate a square root. If we add sqrt%283m-1%29 to each side,
2sqrt%28m-1%29+=+sqrt%283m-1%29
both square roots are now isolated. (This is fortunate. Equations with multiple square roots often require two rounds of step #1 and step #2.)
2) Square both sides:
%282sqrt%28m-1%29%29%5E2+=+%28sqrt%283m-1%29%29%5E2
2%5E2%2Asqrt%28m-1%29%5E2+=+%28sqrt%283m-1%29%29%5E2
4%28m-1%29+=+3m-1
3) Both square roots are gone! So we can proceed to step #4.
4) Solve the equation. This is a very simple equation to solve. First we simplify:
4m-4+=+3m-1
Subtract 3m from each side:
m+-+4+=+-1
Add 4 to each side:
m+=+3
5) Check the solution(s) in the original equation
2sqrt%28m-1%29+-+sqrt%283m-1%29=0
Checking m = 3:
2sqrt%28%283%29-1%29+-+sqrt%283%283%29-1%29=0
2sqrt%282%29+-+sqrt%288%29=0
At first this may look like it doesn't check. But we can simplify sqrt%288%29:
2sqrt%282%29+-+sqrt%284%2A2%29=0
2sqrt%282%29+-+sqrt%284%29%2Asqrt%282%29=0
2sqrt%282%29+-+2sqrt%282%29=0
Check!

So the only solution is m=3.