Mqt 1001 travail #3
1840 mots
8 pages
Question 1 (15 points)Résolvez les équations ou les inéquations suivantes (chaque sous-question vaut 5 points). Détaillez les étapes de vos calculs, y compris la validation de vos solutions dans le cas des équations.
a) (x + 25 / x+ 5) = (2x + 75 / 2x – 15)
Produits croisé
(x + 25) (2x -15) = (x + 5) (2x +75)
(x × 2x) (x × -15) (25 × 2x) (25 × -15) = (x × 2x) (x × 75) (5 × 2x) (5 × 75)
2x2 + -15x + 50x – 375 = 2x2 + 75x + 10x + 375
(2x2 - 2x2) (35x – 85x) (-375 – 375) = 0
X2 – 50x -750 = 0
Validation :
Formule : x = -b ± √b2 4ac / 2a
X2 – 50x -750 = 0
A B C
X = (-50) + √ (-50)2 – 4 x 1 x (-750) / 2 x 1
X = 50 + √2 500 – (-3 000) / 2
X = 50 + 74, 16198 / 2 ou en moins…. X = 50 – 74, 16198 / 2
X = 124, 16198 / 2 x = -24, 16198 / 2
X = 62, 08 x = -12, 08
X2 – 50x -750 = 0
62,082 – 50(62, 08) – 750 = 0
3 854 - 3 104 – 750 = 0
X2 – 50x -750 = 0
-12, 082 – 50(-12, 08) – 750 = 0
146 + 604 – 750 = 0
b) (x+3 / 2x – 7) – (2x – 1 / x – 3) = 0
Produits croisés
(x + 3) (x – 3) = (2x – 7) (2x -1)
(x × x) (x × -3) (3 × x) (3× -3) = (2x × 2x) (2x × -1) (-7 × 2x) (-7 × -1)
X2 -3x + 3x – 9 = 4x2 – 2x – 14x + 7
X2 – 9 = 4x2 – 16x + 7
(x2 – 4x2) + 16x (-9 -7) = 0
-3x2 + 16x – 16 = 0 A B C
Validation :
Formule : x = -b ± √b2 4ac / 2a
X = (-16) + √ (-16)2 – 4 x -3 x (-16) / 2 x -3
X = -16 + √256 – 192 / -6
X = -16 + √64 / -6 ou en moins…. X = -16 - √256 – 192 / -6
X = -16 + 8 / -6 x = -16 - 8 / -6
X = -8/-6 x = -24/ -6 = 4
-3x2 + 16x – 16 = 0
-3(4)2 + 16(4) – 16 = 0
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