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  4. (x -1) (x2 - 5x + 7) < (x -,1), then x belongs to

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Q. $(x -1) (x^2 - 5x + 7) < (x -,1),$ then $x$ belongs to

BITSATBITSAT 2007

Solution:

Given that, $(x-1)\left(x^{2}-5 x+7\right)<(x-1)$
$\therefore (x-1)\left(x^{2}-5 x+6\right)< 0$
$\Rightarrow (x-1)(x-2)(x-3)< 0 $
$\Rightarrow x \in(-\infty, 1) \cup(2,3)$