si a = (1+ rac(5) /2 alors a² = (1 +2rac(5)+5)/ 4 =(6+2rac(5))/4
=(3+rac(5))/2 or
a+1=(1+rac(5))/2 +2/2 = (3+rac(5))/2 =a²
la reponse est donc oui car a+1=a² ( donc a²-a-1=0)
si b=(1-rac(5) /2 alors
1/b = 2 / (1-rac(5) ) = 2(1+rac5) /((1-rac(5)*(1+rac(5)) =(2+2rac(5) )/(1-5) 1/b= (2+2rac(5) /(-4)= (-1-rac(5)) /2
et 1+1/b = 2/2 +(-1-rac(5))/2 =(1-rac(5))/2 =b la reponse est oui 3) ab = (1+rac(5) /2 *(1-rac(5))/2 =(1-5)/ 4 = -4/4 = -1 on en deduit que -ab = 1 puis que -b= 1/a la reponse est bien oui