Réponses

2014-04-09T23:29:47+02:00
Bonsoir,

a) x² = 9
x² - 9 = 0
x² - 3² = 
(x - 3)(x+ 3) = 0
x - 3 = 0   ou   x + 3 = 0
x = 3   ou   x = -3

b)  x^2=\dfrac{25}{16}\\\\x^2-\dfrac{25}{16}=0\\\\x^2-(\dfrac{5}{4})^2=0\\\\(x-\dfrac{5}{4})(x+\dfrac{5}{4})=0\\\\x-\dfrac{5}{4}=0\ \ ou\ \ x+\dfrac{5}{4}=0\\\\x=\dfrac{5}{4}\ \ ou\ \ x=-\dfrac{5}{4}

c) x^2=5\\\\x^2-5=0\\\\x^2-(\sqrt{5})^2=0\\\\(x-\sqrt{5})(x+\sqrt{5})=0\\\\x-\sqrt{5}=0\ \ ou\ \ x+\sqrt{5}=0\\\\x=\sqrt{5}\ \ ou\ \ x=-\sqrt{5}

d) x² = 0
x = 0

e) x² = -16 est une équation impossible car un carré n'est jamais négatif.

f) 4x² = 49
4x² - 49 = 0
(2x)² - 7² = 0
(2x - 7)(2x + 7) = 0
2x - 7 = 0   ou   2x + 7 = 0
2x = 7   ou   2x = -7
x = -7/2   ou   x = -7/2