SOLUTION: square root 2x+3 - square root x+1 =1

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Question 97303This question is from textbook College Math
: square root 2x+3 - square root x+1 =1 This question is from textbook College Math

Answer by mathslover(157) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%282x%2B3%29 - sqrt%28x%2B1%29 =1
sqrt%282x%2B3%29 = 1+ sqrt%28x%2B1%29
squaring both sides of the equation we get
2x+3 = 1 + 2sqrt%28x%2B1%29 + x+1
2x+3 -x -2 = 2sqrt%28x%2B1%29
x + 1 = 2sqrt%28x%2B1%29
squaring both sides again
x^2 + 2x +1 = 4(x+1)
x^2 -2x -3 =0
Using x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
we have
x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%2A1%2A%28-3%29+%29%29%2F%282%2A1%29+
x= (2-4)/2 and (2+4)/2
x= -1 and 3