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Question
Write the set of values of x satisfying the inequation (x2 − 2x + 1) (x − 4) < 0.
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Solution
We have:
\[\left( x^2 - 2x + 1 \right)\left( x - 4 \right) < 0\]
\[ \Rightarrow (x - 1 )^2 (x - 4) < 0\]
\[\text{ Equating each one to zero, we obtain } x = 1 \text{ and } x = 4 . \]
\[\text{ Therefore, 1 and 4 are critical points } . \]
\[\text{ Drawing the number lines, we get }:\]
\[\text{ Therefore, the solution set of the given inequality is x } \in \left( - \infty , 1 \right) \cup \left( 1, 4 \right)\]
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