Réponse :
Explications étape par étape
Bonjour
Factoriser :
f(x) = 2x^2 + 3x - 2
X1 = (-3 - 5)/(2 * 2) = -8/4 = -2
X2 = (-3 + 5)/(2 * 2) = 2/4 = 1/2
f(x) = (x + 2)(x - 1/2)
g(x) = 2x^2 - 9x + 4
X1 = (9 - 7)/(2 * 2) = 2/4 = 1/2
X2 = (9 + 7)/4 = 16/4 = 4
g(x) = (x - 1/2)(x - 4)
2) résoudre :
1/f(x) + x/g(x) = 0
1/[(x + 2)(x - 1/2)] + x/[(x - 1/2)(x - 4)] = 0
[x - 4 + x(x + 2)]/[(x + 2)(x - 1/2)(x - 4)] = 0
(x^2 + 3x - 4)/[(x + 2)(x - 1/2)(x - 4)] = 0
[tex]x + 2 \ne 0[/tex]
[tex]x \ne -2[/tex]
[tex]x - 1 \ne 0[/tex]
[tex]x \ne 1[/tex]
[tex]x - 4 \ne 0[/tex]
[tex]x \ne 4[/tex]
x^2 + 3x - 4 = 0
x^2 + 2 * x * 3/2 + (3/2)^2 - (3/2)^2 - 4 = 0
(x + 3/2)^2 - 9/4 - 16/4 = 0
(x + 3/2)^2 - 25/4 = 0
(x + 3/2)^2 - (5/2)^2 = 0
(x + 3/2 - 5/2)(x + 3/2 + 5/2) = 0
(x - 2/2)(x + 8/2) = 0
(x - 1)(x + 4) = 0
x - 1 = 0 ou x + 4 = 0
x = 1 ou x = -4
