Bonjour,
EXERCICE 1
1) (2V6 - 2V7) ² = 4*6 - 8V42 + 4*7 = 24 - 8V2 + 28 = 52 - 8V2
2) (4V5 - 5V3) ² = 16*5 - 40V15 + 25*3 = 80 - 40V15 + 75 = 155 - 40V15
3) (4 + 2V2) (4 - 2V2) = 4² - (2V2)² = 16 - 4*2 = 16 - 8 = 8
4) [tex]\dfrac{36\sqrt{20}}{8\sqrt{45}}=\dfrac{36\times2\sqrt{5}}{8\times3\sqrt{5}}=\dfrac{72}{24}=3[/tex]
EXERCICE 2
1) -2V112 + V63 - 2V28 = -2V(16*7) + V(9*7) - 2V(4*7) = -2*4V7 + 3V7 - 2*2V7
= -8V7 + 3V7 - 4V7 = -9V7
2) V32 x V8 x V18 = V(16*2) * V(4*2) * V(9*2) = 4V2 * 2V2 * 3V2 = 4*2*3*2V2 = 48V2
3) (4V5 - 4V6) ² = 16*5 - 32V30 + 16*6 = 80 - 32V30 + 96 = 176 - 32V30
4) (2V5 - 3V7) ² = 4*5 - 12V35 + 9*7 = 20 - 12V35 + 63 = 83 - 12V35
5) (3 + 5V5) (3 - 5V5) = 3² - (5V5)² = 9 - 25*5 = 9 - 125 = -116
6) [tex]\dfrac{18\sqrt{8}}{4\sqrt{18}}=\dfrac{18\sqrt{4\times2}}{4\sqrt{9\times2}}=\dfrac{18\times2\sqrt{2}}{4\times3\sqrt{2}}=\dfrac{36}{12}=3[/tex]
EXERCICE 3
1) -3V112 + 3V63 + 4V28 = -3V(16*7) + 3V(9*7) + 4V(4*7) = -3*4V7 + 3*3V7 + 4*2V7
= -12V7 + 9V7 + 8V7 = 5V7
2) V20 x V80 x v45 = V(4*5) * V(16*5) * V(9*5) = 2V5*4V5*3V5 = 2*4*3*5*V5 = 120V5
3) (4V3 + 3V7) ² = 16*3 + 24V21 + 9*7 = 48 + 24V21 + 63 = 111 + 24V21
4) (3V10 - 4V3) ² = 9*10 - 24V30 + 16*3 = 90 - 24V30 + 48 = 138 - 24V30
5) (3 + 5V10) (3 - 5V10) = 3² - (5V10)² = 9 - 25*10 = 9 - 250 = -241
6) [tex]\dfrac{48\sqrt{45}}{9\sqrt{80}}=\dfrac{48\sqrt{9\times5}}{9\sqrt{16\times5}}=\dfrac{48\times3\sqrt{5}}{9\times4\sqrt{5}}=\dfrac{144}{36}=4[/tex]
