Solution of the equation $\sqrt {x + 3 - 4\sqrt {x - 1} }  + \sqrt {x + 8 - 6\sqrt {x - 1} }  = 1$ is

  • A

    $x \in \left[ {4,9} \right]$

  • B

    $x \in \left[ {3,8} \right]$

  • C

    $x \in \left[ {5,10} \right]$

  • D

    $x \in \left[ {4,7} \right]$

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$I$. For any $n$, the roots are distinct.

$II$. There are infinitely many values of $n$ for which both roots are real.

$III$. The product of the roots is necessarily an integer.

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