Cours de mathématiques de collège
RADICAUX
- Définition
- \(a\) étant positif, \((\sqrt{a})^2 = a\)
- Propriétés
- \(\sqrt{ab} = \sqrt{a} \times \sqrt{b}\)
- \(\sqrt{a^2b} = a \times \sqrt{b}\)
- \(\frac{a}{\sqrt{b}} = a \times \frac{\sqrt{b}}{b}\)
- \(\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}\)
- \(\frac{a + b}{\sqrt{c} + \sqrt{d}} = (a + b) \times \frac{\sqrt{c} - \sqrt{d}}{(\sqrt{c} + \sqrt{d}) \times (\sqrt{c} - \sqrt{d})}\)
- Résolution
- \(x^2 = a\)
- Il y a DEUX solutions : \(x = \sqrt{a}\) ET \(x = - \sqrt{a}\)
- Trois cas possibles
- \(a > 0 => x = \sqrt{a}\) ET \(x = - \sqrt{a}\)
- \(a = 0 => x^2 = 0 => x = 0\)
- \(a < 0 =>\) AUCUNE SOLUTION