SOLUTION: Solve the equation sqrt (2x + 5) - sqrt (x - 2) = 3

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Question 172937This question is from textbook Introductory Algebra
: Solve the equation
sqrt (2x + 5) - sqrt (x - 2) = 3 This question is from textbook Introductory Algebra

Found 2 solutions by monika_p, Mathtut:
Answer by monika_p(71)   (Show Source): You can put this solution on YOUR website!
if you have variable inside a square root you have to do the opposit operation :squaring to "take out" x from root
[example ]
square both sides of the equation

2x+5-(x-2)=9
x=2 answer
Answer by Mathtut(3670)   (Show Source): You can put this solution on YOUR website!
although the answer is partially correct shown by monika ..she is missing a solution and got fortunate(or unfortunate depending on how you see it) to find the solution of 2. Why?? because when you do one thing to one side of the equation you have to do the same to the other....when you have one term to square on each side of the equals sign it is easy but when there are two terms which are added or subtracted......they must be taken as a whole and squared....you CANNOT square each term seperately unless the terms are multiplied together....with that in mind lets proceed to solve the problem. It is an easy mistake to make and is made quite often.
:
given
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radicalize by squaring both sides
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multiplying out the squares
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combining like terms on left side of eq
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combining like terms in the equation
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squaring both sides to radicalize again
:
squaring left removed radical...mult.right side
:
multiplied part of left side
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multiplied out rest of left side
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combined like terms
:
answers
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=1296 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 38, 2. Here's your graph:
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