bjr
1)
A = 5/14 + (9/14)x(7/5) - 2/5
= 5/14 + (9x7)/(14x5) - 2/5
= 5/14 + (9x1)/(2x5) - 2/5 (on simplifie par 7)
= 5/14 + 9/10 - 2/5 (dénominateur commun 70)
= 25/70 + 63/70 - 28/70
= (25 + 63 - 28)/70
= 60/ 70
= 6/7
2)
√48 = √(16 x 3) = √16 x √3 = 4√3
√75 = √(25 x 3) = √25 x √3 = 5√3
B = -2(4√3) + 5√3
= -8√3 + 5√3
= (-8 + 5)√3
= -3√3
3)
(2x - 3)(x + 5) = (double distributivité)
2x*x + 2x*5 - 3*x - 3*5 =
2x² +10x - 3x - 15 =
2x² + 7x - 15
(x + 2)² = [on utilise (a + b)² = .... ]
x² + 2*2x + 2² =
x² + 4x + 4
C = 2x² + 7x - 15 - (x² + 4x + 4)
= 2x² + 7x - 15 - x² - 4x - 4
= x² + 3x - 19
4)
D = 25 - (3x - 4)² = (différence de deux carrés)
5² - (3x - 4)² =
[5 - (3x - 4)][5 + (3x - 4)] =
(5 - 3x + 4)(5 + 3x - 4) =
(-3x + 9)(3x + 1) =
3(-x + 3)(3x + 1)
5)
45 + 45 x 3/100 = 45 + 1,35 = 46,35 (€)
