SOLUTION: Hi, I am having doubts that I solved this problem correctly. Here is my work. (square root of x + 2) - 2 = (square root of x + 9) i squared both sides. x + 9 = x + 2 - (14squar

Algebra ->  Radicals -> SOLUTION: Hi, I am having doubts that I solved this problem correctly. Here is my work. (square root of x + 2) - 2 = (square root of x + 9) i squared both sides. x + 9 = x + 2 - (14squar      Log On


   

Question 170720This question is from textbook
: Hi,
I am having doubts that I solved this problem correctly. Here is my work.
(square root of x + 2) - 2 = (square root of x + 9)
i squared both sides.
x + 9 = x + 2 - (14square root of x + 2) + 49
9 = 51 -(14square root of x + 2)
-42= square root of x + 2
1764 = x + 2
x = 1762
when I substitute 1762 into the original equation and found it to be extraneous. Is this correct?
This question is from textbook

Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
I am having doubts that I solved this problem correctly. Here is my work.
(square root of x + 2) - 2 = (square root of x + 9)
i squared both sides.
x + 9 = x + 2 - (14square root of x + 2) + 49
9 = 51 -(14square root of x + 2)
-42= square root of x + 2
1764 = x + 2
x = 1762
when I substitute 1762 into the original equation and found it to be extraneous. Is this correct?
--------------------
sqrt(x + 2) - 2 = sqrt(x + 9)
Square both sides
x+9 = (x+2) +4 -4sqrt(x+2)
-4sqrt(x+2) = x+9 -x-2 -4 = 3
Square again
16*(x+2) = 9
x+2 = 9/16
x = -23/16
-------------
It does check if you take into account the + and - on the sqrts.




Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
(square root of x + 2) - 2 = (square root of x + 9)
----------------
You did well to check your answer.
----------------
sqrt(x+2) -2 = sqrt(x+9)
Square both sides to get:
x+2 -4sqrt(x+2) + 4 = x+9
Simplify
-4sqrt(x+2) + 6 = 9
sqrt(x+2) = -3/4
---------
Square both sides to get:
x+2 = 9/16
x = -23/16
----------------
Checking the answer:
sqrt(x+2) -2 = sqrt(x+9)
sqrt(9/16) -2 = sqrt(121/16)
3/4 - 8/4 = 11/4
-5/4 = 11/4
This is wrong so x = -23/16 is not a solution.
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Comment: there is no solution for the problem you have posted.
You can see that if you graph the left side and the right
side separately; They have no point of intersection.
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Cheers,
Stan H.