bonjour aidez-moi à résoudre ce devoir​

Réponse :

Explications étape par étape

Bonsoir

a = V6 + 3

b = V6 - 3

Calculer :

a^2 = (V6 + 3)^2 = 6 + 6V6 + 9 = 15 + 6V6

a x b = (V6 + 3)(V6 - 3) = 6 - 9 = -3

a - b = V6 + 3 - V6 + 3 = 6

Rendre rationnel a/b :

a/b = (V6 + 3)/(V6 - 3)

a/b = (V6 + 3)(V6 + 3) / (V6 - 3)(V6 + 3)

a/b = (15 + 6V6)/(-3)

a/b = -5 - 2V6

a = 9 + 2V14

b = 9 - 2V14

Calculer :

a^2 = (9 + 2V14)^2 = 81 + 36V14 + 4 * 14 = 81 + 56 + 36V14 = 137 + 36V14

a x b^(-1) = (9 + 2V14)(9 - 2V14)^(-1) = (9 + 2V14)(9 + 2V14)/(9 - 2V14)(9 + 2V14) = (137 + 36V14) / 25

a x b = (9 + 2V14)(9 - 2V14) = 81 - 4 * 14 = 81 - 56 = 25

a - b = 9 + 2V14 - 9 + 2V14 = 4V14

Va + Vb = V(9 + 2V14) + V(9 - 2V14)