td03

2 T D02
◦ ◦
◦ ◦ ♥x+y= 7 x2+y2= 29 x y
x+y= 7 x3+y3= 215
a b x +y=a x3+y3=b x y
◦ ◦
◦ ◦ ]
◦ ◦
◦ ◦ f[0,1] Rf(0) = 0 f(1) = 2
∀x∈[0,1],06f(x)62f
◦ ◦
◦ ◦ 2 10110011 11001101
◦ ◦
◦ ◦ ♥cos4(θ)−sin4(θ) = √3θ
◦ ◦
◦ ◦ ♥cos(π/12) cos π
3−π 4√6 + √2 4
2.cos2(π/12) −1 = cos(π/6) r√3+2
4
◦ ◦
◦ ◦ ]
◦ ◦
◦ ◦ ♥X3−4.X2+ 3.X + 6 a b c
3a.b a.c b.c
(a.b)2(a.c)2(b.c)2
2013 2014
◦ ◦ λ X3−7.X2+ 8.X +λ
◦ ◦
◦ ◦ ♣ii= (ei.π/2)i=ei2.π/2=1
√eπ
◦ ◦
◦ ◦ 5.X3−67.X2+ 244.X −224
◦ ◦
◦ ◦ ♥cos(a) + cos(b)
sin(a) + sin(b)
◦ ◦
◦ ◦ 100
k17 k0 100
◦ ◦
◦ ◦ ♣2013 10 10111011111 2 2013 = 2.103+ 1.101+
3.100= 210 + 28+ 27+ 26+ 24+ 23+ 22+ 21+ 20−10
◦ ◦
◦ ◦ ♠32.x3+ 144.x2+ 210.x + 92 = 0 x
32.y3+p.y +q= 0 (y=x+. . .)
4.z3−3.z =a z =α.y
z= cos(θ)

z=
u+1
u
2u
u3U
U u
z1z2z33
x1x2x3
◦ ◦
◦ ◦ σ{1,2,3,4, . . . 12}
k1 2 3 4 5 6 7 8 9 10 11 12
σ(k) 8 4 5 3 4 7 6 12 11 1 2 ∗
σ◦σ σ ◦σ◦σ σ ◦. . .◦σ=Id
◦ ◦
◦ ◦ a b c d e
a.b +b.c +c.d +d.e +e.a
2013 2014
◦ ◦ ♥j e2.i.π/3j2013
A=
2013
X
k=0
jkB=
2013
X
k=0 2013
k.jk
C=
2013
X
p=0 2013
k.jkD=
2013
X
k=0 2013
k.jp
E=
2013
X
k=0 2013
p.jkF=
2013
X
k=0 2013
p.jp
X
p≤2013
k≤2013
2013
p.jk20142
◦ ◦
◦ ◦ a0,123412341234 . . . 1234
1000.a −a a p/q p q
◦ ◦
◦ ◦ ♥P4 3 1
6P0(0) = −3P0
PP(0) P
◦ ◦
◦ ◦
(1 + 5.i)4
1 + 239.i
2013 2014
◦ ◦ ♥6.cos2(x)−5.cos(x) + 1 = 0 x0
2.π −2.π 5.π
♣
◦ ◦
◦ ◦ ♣α(aαb)⇔(tan(a)≤tan(b)) Z
• ∀ a∈Z, aαa
•∀ (a, b)∈Z2,(aαb)et (bαa)⇒(a=b)
•∀ (a, b, c)∈Z3,(aαb)et (bαc)⇒(aαc)
◦ ◦

◦ ◦ ♥(a, b)−→ (2.a +b, a −b)Z×Z
(1,1)
(a, b)−→ (2.a + 3.b, a +b)
(a, b)−→ (Min(a, b), a + 2.b)N×N
f A B B
∀b∈B, ∃a∈A, f(a) = b
◦ ◦
◦ ◦ ♣
6
Y
k=0
(kk).k! = (6!)7
(n!)2(2.n)!
◦ ◦
◦ ◦ ♠♣ a b c d X4−4.X3+ 2.X2−X+ 1
a2.b2
•a.b.c
•
•
◦ ◦
◦ ◦ ♣2014 n! 2014n! 2014
n! 2014 n!