Question

Stiind ca a-1/a=3,a apartine nr reale nenule.Aratati ca a la patrat+1/a la patrat=11

Answer 1

Răspuns:

Explicație pas cu pas:

$a-\dfrac{1}{a} =3~|^2\\(a-\dfrac{1}{a})^{2}=3^{2}\\a^{2}-2*a*\dfrac{1}{a}+(\dfrac{1}{a})^{2}=9,~~ a^{2}-2+(\dfrac{1}{a})^{2}=9,\\a^{2}+\dfrac{1}{a^{2}}=9+2=11$