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Meilleure réponse !
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  • Modérateur confirmé
2014-03-18T23:08:25+01:00
Salut,

Exercice 12
a)
x² = 4/9
x² - 4/9 = 0
x² - (2/3)² = 0
(x-2/7)(x+2/7) = 0
x - 2/7 = 0
x = 2/7
x +2/7 = 0
x = -2/7

S = {-2/7; 2/7}

b)

x² = 1/16
x² - 1/16 = 0
x² - (1/4)² = 0
(x+1/4)(x-1/4) = 0
x+1/4 = 0
x = - 1/4
x-1/4 = 0
x = 1/4

S = {-1/4; 1/4}

c)

x² = - 64/9
Impossible, x² toujours positif, donc x² ≥ 0

d)

x² = 11/4
x² - 11/4 = 0
(x-(√11)/2)(x+(√11)/2 ) = 0

x - (√11)/2 = 0
x = (√11)/2

x + (√11)/2 ) 0
x = -(√11)/2

S = { - (√11)/2; (√11)/2}

Exercice 13

a)
x² -100 = 0
(x-10)(x+10) = 0
x - 10 = 0
x = 10
x + 10 = 0
x = -10

S = {-10; 10}
b)
x² + 25 = 0
Impossible.

c)

x² - 9/16 = 0
(x+3/4)(x-3/4) = 0
x + 3/4 = 0
x = -3/4
x - 3/4 = 0
x = 3/4

S = {-3/4; 3/4}

Exercice 14:

4x² = 36
x² = 36/4 = 9
x² - 9 = 0
(x+3)(x-3) = 0
x + 3 = 0
x = -3
x-3=0
x = 3

S={-3; 3}

7x² = 49
x² = 7
x² - 7 = 0
(x-√7)(x+√7) = 0
x - √7 = 0
x = √7

x + √7 = 0
x = - √7

S = {-√7; √7}

6x² = 96
x² = 96/6 = 16
x² - 16 = 0
(x+4)(x-4) = 0

x + 4 =0
x = -4

x-4=0
x = 4

S ={-4;4}

-2x² = 24
x² = 24/(-2) = -12
x² + 12 = 0

Impossible.


Bonne soirée !