Question

$x^2-6x+5\le 0,x^2-2x$> 0 where $x$ is an integer. Find all the possible values of $x$.

• A. Only 4, 5
• B. Only 1, 5
• C. Only 3, 4, 5
• D. Only 1, 3, 5

Answer 1

The correct option is C

Only 3, 4, 5

$x^2-6x+5\le 0\Rightarrow (x-1)(x-5)\le 0$
$\Rightarrow 1\le x\le \mathrm{5......}\left(1\right)$
$x^2-2x$ > $0\Rightarrow x(x-2)$ > $0\Rightarrow x$ < 0 or x > 2.....(2)
From (1) & (2), 2 < x $\le 5$
$\Rightarrow x=3,4,5$