Question

Write the set of values of x satisfying the inequation (x² − 2x + 1) (x − 4) < 0.

Answer 1

We have:Therefore, the solution of the given inequality is x∈(2,∞)

$$\begin{gathered} \left(x^2-2x+1\right)\left(x-4\right)<0 \\ \Rightarrow (x-1{)}^2(x-4)<0 \\ \mathrm{Equating}\mathrm{each}\mathrm{one}\mathrm{to}\mathrm{zero},\mathrm{we}\mathrm{obtain}\mathrm{x}=1\mathrm{and}\mathrm{x}=4. \\ \mathrm{Therefore},1\mathrm{and}4\mathrm{are}\mathrm{critical}\mathrm{points}. \\ \mathrm{Drawing}\mathrm{the}\mathrm{number}\mathrm{lines},\mathrm{we}\mathrm{get}: \end{gathered}$$


$\mathrm{Therefore},\mathrm{the}\mathrm{solution}\mathrm{set}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{inequality}\mathrm{is}x\in \left(-\infty ,1\right)\cup \left(1,4\right)$herefore, the solution of the given inequality is x∈(2,∞)