Slove the following equation :: Sqrt(x+1)-sqrt(x-1) = sqrt(4x-1)

Question

Sqrt(x+1)-sqrt(x-1) = sqrt(4x-1) , we get the solution after solving as x=5/4 . But when we subsitute x=5/4 back in the equation we get 1=2 . Why ??

Answer 1

squaring both sides we get

(x+1) + (x-1) -2*sqrt(x^2-1)== 4x-1

            sqrt(x^2-1)==  .5 - x

      since sqrt of any function is positive hence .5 - x >0

                                                       x<.5

but our solution was x=5/4 ,, hence it has NO Solution .

Comments

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Answer 2

Sqrt(x+1)-sqrt(x-1) = sqrt(4x-1) , we get the solution after solving as x=5/4
substitute in sqrt(x+1)-sqrt(x-1)=sqrt(4*x-1)

we have a right to write
sqrt(1.25+1)-sqrt(1.25-1)=sqrt(4*1.25-1)
and we also have a right to write
(+/- 1.5) - (+/- 0.25) = +/- 2 and we can choose the symbols to our liking to suit our equation
+1.5 - (-.5)=+2
also -1.5 - (+.5)=-2
which are both true Hence 5/4 is correct answer.