SOLUTION: Solve: sq rt of 3x-5 - sq rt of x+2 = 1

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Question 441834: Solve:
sq rt of 3x-5 - sq rt of x+2 = 1
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
First, square both sides:
%28sqrt%283x-5%29+-+sqrt%28x%2B2%29%29%5E2+=+1%5E2
Applying FOIL on the LHS we have:
%283x-5%29+%2B+%28x%2B2%29+-+2sqrt%28%283x-5%29%28x%2B2%29%29+=+1
Collecting terms and isolating the term with the square root gives:
4x-4+=+2sqrt%28%283x-5%29%28x%2B2%29%29
Isolating the square root term allows us to square both sides again:
%284x-4%29%5E2+=+4%283x-5%29%28x%2B2%29
Performing the multiplcation gives:
16x%5E2+-32x+%2B+16+=+4%283x%5E2+%2B+x+-+10%29
Divide through by 4 and collect terms:
x%5E2+-+9x+%2B+14+=+0
Solve for x using the quadratic formula:
x+=+%289+%2B-+sqrt%2881-56%29%29%2F2 -> x = 2, 7
The squaring operation allows for positive and negative solutions, but only one value of x will make the original expression valid.
Check:
x=2: sqrt%286-5%29+-+sqrt%284%29+=+1+-+2+=+-1 [Discard this solution]
x=7: sqrt%2821-5%29+-+sqrt%289%29+=+4+-+3+=+1 [Correct]
Ans: x = 7