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
Mathématiques
Kailyas
Question
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
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 Réponse
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1. Réponse maudmarine
(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