Missy Myd'

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