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Question 146182: Hello, I need a little help with the following.
Square root of 3x+1 - square root of x+1 = 2. I have tried solving this by isoloating the x+1 square root term, but keep getting a no solution answer, which is not correct. If someone could provide me the steps on how to get the correct answer, so I can learn the steps myself, that would be much appreciated.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Sqrt(3x+1) - sqrt(x+1) = 2.
sqrt(3x+1) = 2 + sqrt(x+1)
Square both sides to get:
3x+1 = 4 + 4sqrt(x+1) + x+1
2x = 4 + 4sqrt(x+1)
x-2 = 2sqrt(x+1)
Square both sides to get:
x^2 -4x+4 = 4x+4
x^2-8x = 0
x(x-8) = 0
x = 0 or x = 8
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Checking:
x=0?
sqrt(1) - sqrt(1) = 2; Wrong
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x=8?
sqrt(25) - sqrt(9) = 2
5-3=2 ; Correct
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Final Solution: x=8
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Cheers,
Stan H.
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