un simple calcule

Si on pose x=a+1/a,on aura a^2+1/a^2=x^2-2
et a^3+1/a^3=x^3-3x , on constate que x=3
a^4+1/a^4=(a^3+1/a^3)(a+1/a)-(a^2+1/a^2)=47