Réponse:
Ex 1
[tex]A= - \frac{5}{4} + \frac{2}{5} + 1 \\ A= - \frac{25}{20} + \frac{8}{20} + \frac{20}{20} \\ A= \frac{3}{20} \\ A=0.15[/tex]
A ∈ ID
[tex]B = \frac{ {7}^{4} }{ {7}^{ - 9} \times {7}^{8} } \\ B = {7}^{4 - ( - 9) - 8} \\ B = {7}^{5} \\ B = 16807[/tex]
B ∈ IN
[tex]C = ( {2}^{ - 3} \times {3}^{ - 1} ) ^{4} \times ( {3}^{ - 1} ) ^{ - 2} \times ( {2}^{3} )^{4} \\ C = {2}^{ - 12} \times {3}^{ - 4} \times {3}^{2} \times {2}^{12} \\ C = {2}^{ - 12 + 12} \times {3}^{ - 4 + 2} \\ C = {2}^{0} \times {3}^{ - 2} \\ C = \frac{1}{ {3}^{2} } \\ C = \frac{1}{9} [/tex]
C ∈ IQ
[tex]D = 3 \sqrt{3} - 2 \sqrt{4 \times 3} + \sqrt{3 \times 100} \\ D = 3 \sqrt{3} - 4 \sqrt{3} +1 0 \sqrt{3} \\ D = 9\sqrt{3} [/tex]
D ∈ IR
[tex]E = 5 \sqrt{4 \times 5} - 3 \sqrt{5 \times 16} + 12 \sqrt{9 \times 5} \\ E = 10 \sqrt{5} - 12 \sqrt{5 } + 36 \sqrt{5} \\ E = 34 \sqrt{5} [/tex]
E ∈ IR
Ex 2
a) 4x ≤ 0 <=> x ≤ 0
x ∈ ]-∞ ; 0]
b)
-4x < 0 <=> x > 0
x ∈ ]0 ; +∞[
c)
6+8x ≥ 4x
8x - 4x ≥ -6
4x ≥ -6
x ≥ -6/4
x ≥ -3/2
x ∈ [-3/2; +∞[
d)
|x| < 3
-3 < x < 3
x ∈ ]-3; 3[
e)
|x-2| ≤ 5
-5 ≤ x-2 ≤ 5
-3 ≤ x ≤ 7
x ∈ [-3; 7]
