Réponse :
Explications étape par étape
Bonjour
b) 9z+4=(z+2)^2
9z + 4 = z^2 + 4z + 4
z^2 + 4z - 9z + 4 - 4 = 0
z^2 - 5z = 0
z(z - 5) = 0
z = 0 ou z - 5 = 0
z = 0 ou z = 5
c) -7t^2+t=8
7t^2 - t + 8 = 0
[tex]\Delta = (-1)^{2} - 4 * 7 * 8 = 1 - 224 = -223 < 0[/tex]
Pas de solution
d) (9v+11)^2-56=3v-1
81v^2 + 198v + 121 - 56 - 3V + 1 = 0
81v^2 + 195v + 66 = 0
[tex]\Delta = 195^{2} - 4 * 81 * 66 = 38025 - 21384 = 16641[/tex]
[tex]\sqrt{\Delta} = 129[/tex] > 0 donc 2 solutions
X1 = (-195 - 129)/(2 * 81) = -324/162 = -2
X2 = (-195 + 129)/(2 * 81) = -66/162 = -11/27
e) (4x+3)^2=(5x-1)^2
(4x + 3)^2 - (5x - 1)^2 = 0
(4x + 3 - 5x + 1)(4x + 3 + 5x - 1) = 0
(-x + 4)(9x + 2) = 0
-x + 4 = 0 ou 9x + 2 = 0
x = 4 ou 9x = -2
x = 4 ou x = -2/9
