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posted by  Katrina Marie on 10/8/2008 10:42:17 PM  |  status: Live  

Equations involving radicals

Question Details:
I have to Solve each equation and check for extraneous solutions. I'm still not sure about these.
 
= 5
 
 

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posted by Leith on 10/8/2008 10:52:07 PM  |  status: Live
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2 √w + 4  = 5

√w+4 = 5/2

w+4 = 25/4

w= 9/4

no extraneous solution
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posted by BIGWILLIEwg on 10/8/2008 10:55:24 PM  |  status: Live
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posted by EMFN on 10/8/2008 11:05:16 PM  |  status: Live
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Response Details:
The first thing you want to do is isolate the radical.
 
That is, place the radical alone on one side of the equation.
 
We can do this by dividing both sides by 2.
 
Doing so we get this equation:
 
 
To remove the radical, we square both sides.
 
 
w + 4 = 25/4
 
Subtracting 4 from both sides we get:
 
w = 25/4 - 4/1
 
w = 9/4
 
How do we know if w = 9/4 is correct? 
 
We plug this into the original equation and simplify.
 
In the radicand, we add and get:
 
 
2() = 5
 
5 = 5
 
The answer for w = 9/4.
 
 
 
 
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