Question 513430: Hi,
I did not get the right answer to the problem
Square root of (3x-2) - Square root of (x+2) = 4
I said:
3x-2 - (x+2) = (4)^2
3x-2 - x - 2 = 16
2x=20
x=10
but when I did the check, the answer is 34. How can I get 34 from this? What did I do wrong?
Thank you so much for finding the time to answer my question.
Sincerely,
I.
Answer by drcole(72)   (Show Source):
You can put this solution on YOUR website! You made a common error: you saw an equation of the form
and thought you could square both side to get rid of the square roots, but this doesn't work (for example,
but 25 - 9 does not equal 2^2 = 4).
The proper technique is to move one of the square roots to the other side of the equation, then square both sides, remembering to FOIL. So in this problem:
 (adding sqrt(x + 2) to both sides)
 (squaring both sides)
 (FOIL!)
 (combine like terms)
At this point, we only have one square root left, but to get rid of it, we need to isolate it to one side of the equation, and then square both sides again.
 (subtracted 18 and x from both sides to isolate square root)
 (square both sides)
 (FOIL on left; distributed 64 on right)
 (combine like terms)
 (subtract 64x and 128 from both sides)
 (divide both sides by 4 to make the coefficient of x^2 to be 1)
 (factor: -2 - 34 = -36, and (-2)(-34) = 68)
Thus the two possible solutions are x = 2 and x = 34. We're not done yet, though, because by squaring, we may have introduced extraneous solutions. We need to check both possible solutions to see if they solve the original equation. Trying x = 2, we get:
for the left hand side, which is not equal to 4, the right hand side. So x = 2 is extraneous: our methods made it look like a possible solution, but it wasn't actually a solution. If we try x = 34 however, we get:
so x = 34 is a solution. Thus x = 34 is the only solution to the original equation.
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