exi....

salut tout le monde
a^3+1/a^3=18
calculut a^4+1/a^4
bonne chance

aussi déja posté plusieur fois
posons x=a+1/a
18=a^3+1/a^3=x(x²-3)=18
<=> x^3-3x-18=0
<=>x^3-27-3x+9=0
<=>(x-3)(x²+3x+9)-3(x-3)=0
<=> x=3 ou x²+3x+6=0 => pas de solution
x=3 <=> a+1/a =3
=>a²+1/a²=7 =>a^4+1/a^4= 47

merci mon ami mathsmaster

posons x=a+1/a
18=a^3+1/a^3=x(x²-3)=18

pourquoi a^3+1/a^3=x(x²-3)[/img]

a^3 +1/a^3 = (a+1/a)(a²-a*1/a+1/a²)=(a+1/a)(a²+1/a²-1)
=(a+1/a)((a+1/a)²-2-1)=x(x²-3)