Salut,
[tex]\left(a+\dfrac{1}a\right)^2=a^2+2\cdot a\cdot\dfrac{1}a+\dfrac{1}{a^2}=a^2+2+\dfrac{1}{a^2}\Rightarrow\\\\\Rightarrow a^2+\dfrac{1}{a^2}=\left(a+\dfrac{1}a\right)^2-2=\left(\dfrac{5}2\right)^2-2=\dfrac{25}4-2=\dfrac{17}4.[/tex]
Green eyes.
