Explications étape par étape :
Bonjour,
a. A = 5
B = 1/2 * ( 5 + 5/5 )
⇔ B = 1/2 * 6
⇔ B = 3
b. C = 1/2 * ( 3 + 5/3 )
⇔ C = 1/2 * 14/3
⇔ C = 7/3
c. D = 1/2 * [ 7/3 + 5/ (7/3) ]
⇔ D = 1/2 * ( 7/3 + 15/7 )
⇔ D = 1/2 * 94/21
⇔ D = 94/42
⇔ D = 47/21
d. E = 1/2 * [ 47/21 + 5/ (47/21) ]
⇔ E = 1/2 * ( 47/21 + 5 * 21/47 )
⇔ E = 1/2 * ( 47/21 + 105/47 )
⇔ E = 1/2 * 4414/987
⇔ E = 4414/1974
⇔ E = 2207/987
2 E² = ( 2207 / 987 )²
⇔ E² ≅ 5
3. A = 23
B = 1/2 * ( 23 + 23/23 )
⇔ B = 1/2 * 24
⇔ B = 12
C = 1/2 * ( 12 + 23/12 )
⇔ C = 1/2 * 167/12
⇔ C = 167/24
D = 1/2 * [ 167/24 + 23 / (167/24) ]
⇔ D = 1/2 * ( 167/24 + 552/167 )
⇔ D = 1/2 * ( 41 137/4008 )
⇔ D = 41 137/8016
E = 1/2 * [ ( 41 137/8016 ) + 23 / ( 41 137/8016 )
⇔ E = 1/2 * ( ( 41 137/8016 ) + 184 368/ 41 137 )
⇔ E = 1/2 * ( 41 137² + 184 368 * 8016)/ ( 8016 * 41 137 )
⇔ E ≅ 4,8068
E² ≅ 23,1
