Question 177767: Please solve
A. (3-√(x+2) )^2=4
and
B. 3+5√(1+2x ^2 )=13
thank you!
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
A. ^2 = 4)
Step 1: Expand the binomial on the left:
 = 4)
Step 2: A simple substitution will allow us to deal with this ugliness in a fairly straightforward manner.
Let  , then:
Step 3: Put the quadratic into standard form:
Giving us a factorable quadratic in t, so:
Step 4: Factor the quadratic:
(t - 5) = 0)
Therefore  or 
But we aren't done yet.
Step 5: Since ,
 
 
 
But we are still not done.
Step 6: Check the potential roots to ensure that we have not introduced extraneous roots in the process of solving the problem:
If  then,
^2 = 4)
^2 = 4)
^2 = 4)
True statement, potential solution confirmed.
If  then,
^2 = 4)
^2 = 4)
^2 = 4)
^2 = 4)
True statement, potential solution confirmed.
Now we are done.
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B. 
Step 1: Add -3 to both sides and then multiply by  to obtain:
Step 2: Square both sides:
Step 3: Add -1 to both sides and then multiply by  to obtain:
Step 4: Take the square root of both sides, considering both the positive and negative roots, and then rationalize the denominators:
Step 5: Check the potential solutions.
Since  regardless of whether  or  , if one solution is good, then they both are:
} = 13)
True statement, both potential solutions  confirmed.
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