SVP Urgent ! Exercice de DM: Résoudre les équations suivantes 1)[tex] x^{2} + 13=48[/tex] 2)[tex]7 x^{2} -11=3 x^{2} +13[/tex] 3)[tex](5x-2) ^{2} =36[/tex] 4)[t

Salut,

x² + 13 = 48
x² = 48 - 13
x² = 35
x² - 35 = 0
(x+[tex] \sqrt{35} [/tex])(x-[tex] \sqrt{35} [/tex]) = 0
x - [tex] \sqrt{35} [/tex] = 0
x = [tex] \sqrt{35} [/tex]
x + [tex] \sqrt{35} [/tex] = 0
x = -[tex] \sqrt{35} [/tex]

7x² - 11 = 3x² + 13
7x² -3x² = 13 +11
4x² = 24
4x² - 24 = 0
(2x - [tex] \sqrt{24} [/tex])(2x+[tex] \sqrt{24} [/tex]) = 0
2x - [tex] \sqrt{24} [/tex] = 0
2x = [tex] \sqrt{24} [/tex]
x = [tex] \sqrt{6} [/tex]
2x+[tex] \sqrt{24} [/tex] = 0
2x = -[tex] \sqrt{24} [/tex]
x = -[tex] \sqrt{6} [/tex]

(5x-2)² = 36
(5x-2)² - 36 = 0
(5x-2+6)(5x-2-6) = 0
(5x +4)(5x-8) = 0
5x + 4 = 0
5x = -4
x = -4/5

5x - 8 = 0
5x = 8
x = 8/5

(3x+2)² = (5x-4)²
(3x+2)² - (5x-4)² = 0
[(3x + 2) - (5x-4)][(3x+2)+(5x-4)] = 0
(3x+2-5x+4)(3x+2+5x-4) = 0
(8x + 6)(8x -2) = 0
2(4x+3)(8x-2) = 0
4(4x+3)(4x-1) = 0
4x + 3 = 0
4x = -3
x = -3/4
4x - 1 = 0
4x = 1
x = 1/4

Bonne soirée !