Bonjour,

on donne deux équations : (x-6)(x+1) = 0 et x^2-3x = 18.
combien ont-elles de solutions communes? Justifier la réponse.

merci

1
bonsoir il suffit que tu realise les deux equation plusieur foi maniere differente (reunie les x aek les x est les nombre de l'autre coter ms n'oublie pas de changer de signe !!!)

Réponses

2014-03-03T22:43:25+01:00
(x + -6)(x + 1) = 0
(-6 + x)(x + 1) = 0
(-6 + x)(1 + x) = 0
(-6 + x) * (1 + x)
(-6(1 + x) + x(1 + x)) = 0
((1 * -6 + x * -6) + x(1 + x)) = 0
((-6 + -6x) + x(1 + x)) = 0
(-6 + -6x + (1 * x + x * x)) = 0
(-6 + -6x + (1x + x2)) = 0
-6x + 1x = -5x (-6 + -5x + x2) = 0
-6 + -5x + x2 = 0
(-1 + -1x)(6 + -1x) = 0

(-1 + -1x)
-1 + -1x = 0 
-1 + 1 + -1x = 0 + 1
-1 + 1 = 0
0 + -1x = 0 + 1
-1x = 0 + 1
0 + 1 = 1 -1
x = 1
x = -1

6 + -1x = 0
6 + -6 + -1x = 0 + -6
6 + -6 = 0
0 + -1x = 0 + -6 -1
x = 0 + -6
-1x = -6
 x = 6

Solutions : x = {-1, 6}


x² - 3x = 18
-3x + x² = 18 
-18 + -3x + x² = 18 + -18
-18 + 18 = 0
-18 + -3x + x² = 0
(-3 + -1x)(6 + -1x) = 0
(-3 + -1x)
-3 + -1x = 0
-3 + 3 + -1x = 0 + 3
-3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3
0 + 3 = 3
-1x = 3
x = -3

(6 + -1x)
6 + -1x = 0
6 + -6 + -1x = 0 + -6
6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6
0 + -6 = -6 -1x = -6
x = 6

Solutions
: x = {-3, 6}


La solution commune est x = 6