Inecuatie cu modul

victoria94 Vin Sept 09, 2011 11:27 pm

rezolvati inecuatia:|x-1-x^2 |<|x^2-3x+4|

**Greatmath** Sam Sept 10, 2011 2:14 am

victoria94 a scris:rezolvati inecuatia: |x-1-x^2 |<|x^2-3x+4|

$\begin{array}{l} \underbrace {\left| {x - 1 - {x^2}} \right| < \left| {{x^2} - 3x + 4} \right|}_{\rm{E}}\\ \left| {x - 1 - {x^2}} \right| = \left| {\left( { - 1} \right)\left[ {{x^2} - x + 1} \right]} \right| = \left| {{x^2} - x + 1} \right| = {x^2} - x + 1,\,\,\forall x \in R\\ \left| {{x^2} - 3x + 4} \right| = {x^2} - 3x + 4,\forall x \in R\\ E \Leftrightarrow {x^2} - x + 1 < {x^2} - 3x + 4 \Leftrightarrow 2x < 3 \Rightarrow x < \frac{3}{2} \end{array}$

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