Réponse :
Bonjour,
Explications étape par étape
1) exercice_3:
a)
1) 2x+3y
10 < x < 15 ==> 20 < 2x <30
6 < y < 12 ==> 18 < 3y < 36
==> 38 < 2x+3y < 66
2)3x-4y
10< x < 15 ==> 30 < 3x < 45
-12 < -y < -6 ==> -48 < -4y < -24
==> -18 < 3x -4y < 21
3) x²+y²
10 < x < 15 ==> 100 < x² < 225
6 < y < 12 ==> 36 < y² < 144
==> 136 < x²+y² < 369
4) (x+1)y
10 < x <15 ==> 11 < x+1 < 16
6 < y < 12
==> 66 < (x+1)*y < 192
b) c²-a²
1 ≤ a ≤ 3 ==> -3 ≤ -a ≤ -1
5 ≤ c ≤ 10
2 ≤ c-a ≤ 9
6 ≤ c+a ≤ 13
12 ≤ (c-a)(c+a)=c²-a² ≤ 117
2) Exercice_4:
[tex]\left\{\begin{array}{ccc}\dfrac{x+2}{y+3} &=&\dfrac{11}{4} \\x+y&=&70\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc|c|c}4x-11y &=&25&1&1 \\x+y&=&70&-4&-11\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}-15y &=&255\\-7x&=&70&-745\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}x &=&\dfrac{745}{7} \\y&=&17\\\end{array}\right.\\\\\\\boxed{\dfrac{x}{y} =\frac{749}{119} }\\[/tex]
