Réponses

2013-06-04T17:38:36+02:00
Exercice 1:
A=9-(-3(2+(-3))+5)
A=9-(-3(2-3)+5)
A=9-(-3*(-1)+5)
A=9-(3+5)
A=9-8=1

B=(7/15)-(2/15)*(9/4)
B=(7/15)-(2*3*3)/(3*5*2*2)
B=(7/15)-(3/10)
B=(14/30)-(9/30)=5/30=1/6

C=5-(9/4)((3/15)+1)-(7/60):(14/-3)
C=5-(9/4)((3/15)+(15/15))-(7/60)*(-3/14)
C=5-(9/4)*(18/15)-(-3*7)/(3*20*2*7)
C=5-(3*3*2*9)/(2*2*3*5)+(1/40)
C=5-(27/10)+(1/40)
C=(200/40)-(108/40)+(1/40)=93/40

Exercice 2:
A=-12x+(4-x)(x+3)-(x+1)(x-3)
A=-12x+4x+12-x^2-3x-(x^2-3x+x-3)
A=-x^2-11x+12-x^2+3x-x+3
A=-2x^2-9x+15

B=(x-3)^2-3x(2x-5)
B=x^2-6x+9-6x^2+15x
B=-5x^2+9x+9

C=((3/5x+(1/5))((-2/5)x+(3/5))-3x(x-4)/25
C=(-6/25)x^2+(9/25)x-(2/25)x+(3/25)-(3x^2-12x)/25
C=(-6/25)x^2+(7/25)x+(3/25)-(3/25)x^2+(12/35)x
C=(-9/25)x^2+(19/25)x+(3/25)

Exercice 3:
a) 3x=-2x+8
3x+2x=8
5x=8
x=8/5

b) 5-2x=-x+7
5-7=-x+2x
-2=x

c) 3x+7-4(1+5x)=18
3x+7-4-20x=18
-17x+3=18
-17x=15
x=-15/17

d) (2/5)(x-4)+1=(3/10)x
(2/5)x-(8/5)+1=(3/10)x
(2/5)x-(3/10)x=(8/5)-(5/5)
(4/10)x-(3/10)x=(3/5)
(1/10)x=(3/5)
x=10*(3/5)=6

e) (x-4)/(x+5)=6
(x-4)=6(x+5)
x-4=6x+30
-4-30=6x-x
-34=5x
x=-34/5

Exercice 4:
A) (5+x)/(7+x)=(4/5)
5(5+x)=4(7+x)
25+5x=28+4x
5x-4x=28-25
x=3

B) on peut donner deux expressions de la somme dont il dispose, ces deux expression étant égales.
S=3x+5
S=4x-2
x étant le prix d'un livre
Donc 3x+5=4x-2
5+2=4x-3x
x=7
Un livre coûte 7€.
Il dispose de S=3*7+5=26€.

Exercice 5:
On note x la longueur AE.
Aire(ABCE)=5x
Aire(DEFG)=2(8-x)
Pour que les aires soient egal il faut que:
5x=2(8-x)
5x=16-2x
5x+2x=16
7x=16
x=16/7