SOLUTION: Solve the equation sqrt (2x + 3) - sqrt (x + 1) = 1

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Question 173614This question is from textbook Introductory Algebra
: Solve the equation
sqrt (2x + 3) - sqrt (x + 1) = 1 This question is from textbook Introductory Algebra

Answer by 303795(602) About Me  (Show Source):
You can put this solution on YOUR website!
Add sqrt+%28x+%2B+1%29 to each side of the equation
sqrt+%282x+%2B+3%29+-+sqrt+%28x+%2B+1%29%2B+sqrt+%28x+%2B+1%29+=+1+%2B+sqrt+%28x+%2B+1%29
sqrt+%282x+%2B+3%29+=+1+%2B+sqrt+%28x+%2B+1%29
Square each side of the equation
%282x+%2B+3%29+=+1+%2B+2%2Asqrt+%28x+%2B+1%29+%2B+%28x%2B1%29
2x+%2B+3+-+1+-+%28x+%2B+1%29+=+1+%2B+2%2Asqrt+%28x+%2B+1%29+%2B+%28x%2B1%29+-+1+-%28x%2B1%29
x+%2B+1++=+2%2Asqrt+%28x+%2B+1%29
Square each side of the equation again
x%5E2+%2B+2x+%2B+1+=+4%2A%28x+%2B+1%29
x%5E2+%2B+2x+%2B+1+=+4x+%2B+4
x%5E2+-+2x+-+3+=+0
%28x+%2B+1%29+%28x+-+3%29+=+0
ie x = -1 or x = 3
Substitute back into the original equation and test if they both work.