Question 113507: Example: Please help me solve this equation:  .
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! solve this equation: .
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The only possible rational roots are +1 and -1
But neither f(1) nor f(-1) is zero.
So, the equation has no rational solutions.
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Cheers,
Stan H.
Answer by Edwin McCravy(20054)  (Show Source):
You can put this solution on YOUR website!
Solution by Edwin
`
As Stanbon says, it has
no rational solutions, but
it can have irrational or
complex solutions,as we'll
see!!
Example: Please help me solve this equation:
We try to see if we can factor that this
as the product of two quadratics:
(__x² + __x + __)(__x² + __ + __}
We know that  factors as  times ,
so we choose 1's for the coefficients of x².
1 factors as either 1×1 or (-1)×(-1).
Since all the terms are positive we chose +1's to go in the
last blanks. So we try to see if we can find A and B such that
the left side factors this way:
For this to be equivalent to the original equation, the
coefficients of like powers must be equal
Since the original equation is
we must have
 and  , or 
Solving the first for  , 
Sunstituting into
So  , and since
So we have now factored te left side of
as
We set each factor = 0, but since
the factors are the same, we only need
set one of them = 0:
Solve that by the quadratic formula and get
x =   and x = 
Each solution has multiplicity 2.
Edwin
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