SOLUTION: Would someone be so kind as to help me out with this problem: sqrt(3x)-1=sqrt(2x+1) Thank you in advance for any help. You all have been a great help in the past.

Algebra ->  Radicals -> SOLUTION: Would someone be so kind as to help me out with this problem: sqrt(3x)-1=sqrt(2x+1) Thank you in advance for any help. You all have been a great help in the past.       Log On


   

Question 327716: Would someone be so kind as to help me out with this problem:
sqrt(3x)-1=sqrt(2x+1)

Thank you in advance for any help. You all have been a great help in the past.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%283x%29-1=sqrt%282x%2B1%29
:
Square both sides, FOIL (sqrt%283x%29-1%29)(sqrt%283x%29-1%29)
:
3x - sqrt%283x%29 - sqrt%283x%29 + 1 = 2x + 1
:
3x - 2sqrt%283x%29 + 1 = 2x + 1
:
3x - 2x + 1 - 1 = 2sqrt%283x%29
:
x = 2sqrt%283x%29
Square both sides
x^2 = 4(3x)
:
x^2 = 12x
Divide both sides by x
x = 12
:
:
Check the solution in original equation; sqrt%283x%29-1=sqrt%282x%2B1%29
Replace x with 12
sqrt%283%2A12%29-1=sqrt%282%2812%29%2B1%29
sqrt%2836%29-1=sqrt%2825%29
6 - 1 = 5; confirms our solution