Question

$(x-1){\left(x-1\right)}^4{\left(x-3\right)}^2\left(x-4\right)>0$
$\left(1,2\right)\cup \left(2,3\right)\cup \left(4,\infty \right)$

Answer 1

Solution :- given,

$\Rightarrow (x-1)(x-1{)}^4(x-3{)}^2(x-4)>0$

$\Rightarrow x-1>0$ or $(x-1{)}^4>0$ or$(x-3{)}^2>0$ or $(x-4)>0$

$\Rightarrow x>1$ or $x>1$ or $x>3$ or $x>4$

$\Rightarrow x\epsilon (1,2)\cup (2,3)\cup (4,\infty )$