SOLUTION: solve the radical equation (2x-1)^1/2=x-2

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Question 87636: solve the radical equation (2x-1)^1/2=x-2
Found 2 solutions by SandySharma, rapaljer:
Answer by SandySharma(35) About Me  (Show Source):
You can put this solution on YOUR website!
%282x-1%29%5E%281%2F2%29=x-2
Squaring both sides, we will get
2x-1+=+%28x-2%29%5E2
2x-1+=+x%5E2+-+4x+%2B+4
Subtract x%5E2 on both sides we will get
2x-1+-+x%5E2+=+-+4x+%2B+4
Add 4x on both sides we will get
2x-1+-+x%5E2+%2B+4x+=+4
6x-1+-+x%5E2+=+4
Subtract 4 on both sides we will get
6x-1+-+x%5E2+-+4=+0
-+x%5E2+%2B+6x+-+5=+0
divide by -1 , we will get
x%5E2+-+6x+%2B+5=+0
Now factorize it
(x - 5)(x-1) = 0
x = 5, 1

Answer by rapaljer(4551) About Me  (Show Source):
You can put this solution on YOUR website!
%282x-1%29%5E%281%2F2%29=x-2

Square both sides:
2x-1=+%28x-2%29%5E2
2x-1+=+x%5E2+-4x%2B4

It's a quadratic equation, so set equal to zero by subtracting 2x and adding +1 to each side of the equation:
2x-1+-2x%2B1+=+x%5E2+-4x+%2B4+-2x+%2B1+
0=x%5E2+-6x+%2B5

Which FACTORS!! (They all do when solving radical equations!!)
0=%28x-5%29%28x-1%29+
x=5 or x=1

Answers are NOT guaranteed, so you need to check the answers in the original equation to see if they work!

x=5
%282x-1%29%5E%281%2F2%29=x-2
%2810-1%29%5E%281%2F2%29=5-2 It checks!!

x=1
%282x-1%29%5E%281%2F2%29=1-2
%282-1%29%5E%281%2F2%29=x-2
1%5E%281%2F2%29+=+-1 Reject. This does NOT check!!

The answer is x=5.

R^2 Retired from SCC