Réponse :
Bonjour,
a)
[tex]x^2 - 49 = 0\\\\\Leftrightarrow x^2 - 7^2 = 0\\\\\Leftrightarrow (x - 7)(x + 7) = 0\\\\[/tex]
[tex]Or \ A \times B = 0 \Leftrightarrow A = 0 \ ou \ B = 0[/tex]
[tex]x - 7 = 0\\\\\Leftrightarrow x = 7\\\\ou\\\\x + 7 = 0\\\\\Leftrightarrow x = -7[/tex]
[tex]Donc \ S = \{-7 \ ; 7 \ \}[/tex]
b)
[tex]9x^2 - 36 = 0\\\\\Leftrightarrow (3x)^2 - 6^2 = 0\\\\\Leftrightarrow (3x - 6)(3x + 6) = 0\\\\\Leftrightarrow 3 \times 3 \times (x - 2) \times (x + 2) = 0\\\\\Leftrightarrow 9(x - 2)(x + 2) = 0[/tex]
[tex]Or \ 9 AB = 0 \Leftrightarrow A = 0 \ ou \ B = 0[/tex]
[tex]x - 2 = 0\\\\\Leftrightarrow x = 2\\\\ou\\\\x + 2 = 0\\\\\Leftrightarrow x = -2[/tex]
[tex]Donc \ S = \{-2 \ ; 2 \ \}[/tex]
c)
[tex]25x^2 = 4\\\\\Leftrightarrow (5x)^2 - 2^2 = 0\\\\\Leftrightarrow (5x - 2)(5x + 2) = 0\\\\[/tex]
[tex]Or \ A \times B = 0 \Leftrightarrow A = 0 \ ou \ B = 0[/tex]
[tex]5x - 2 = 0\\\\\Leftrightarrow 5x = 2\\\\\Leftrightarrow x = \dfrac{2}{5}\\\\ou\\\\5x + 2 = 0\\\\\Leftrightarrow 5x = -2\\\\\Leftrightarrow x = -\dfrac{2}{5}[/tex]
[tex]Donc \ S = \left\{-\dfrac{2}{5} \ ; \dfrac{2}{5} \ \right\}[/tex]
d)
[tex]4x^2 + 4x + 1 = 0\\\\\Leftrightarrow (2x)^2 + 2 \times 2x \times 1 + 1^2 = 0\\\\\Leftrightarrow (2x + 1)^2 = 0[/tex]
[tex]Soit \ 2x + 1 = 0\\\\\Leftrightarrow 2x = -1\\\\\Leftrightarrow x = -\dfrac{1}{2}[/tex]
[tex]Donc \ S = \left\{-\dfrac{1}{2}\right\}[/tex]
