SOLUTION: √(x+2√(x-1)) + √(x-2(√x-1))=x-1
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Question 1085982: √(x+2√(x-1)) + √(x-2(√x-1))=x-1
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
If those expressions have to be defined,
it must be .
There are too many square roots for me to write there,
so I am going to say that
to make the expressions simpler.
If , then
, and .
With that change of variable, the equation turns into
If , then those square roots are
and .
In that case the equation simplifies to
,
,
and since , we can divide both sides by y to get
.
That would mean ,
, and .
There is also the possibility that .
In that case, , and
From the beginning we knew that ,
so ,
,
, and
the equation simplifies to
,
.
However, that equation has no solutions with ,
so there are no more solutions.
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