Stie cineva acest tip de excertitiu? Trebuie sa dea 6 mie mi a dat 62 nu stiu la ce gresesc

Salut,

[tex]\left(a+\dfrac{1}a\right)^2=a^2+2\cdot a\cdot\dfrac{1}a+\left(\dfrac{1}a\right)^2=a^2+2+\left(\dfrac{1}a\right)^2=a^2+\dfrac{1}{a^2}+2\Rightarrow\\\\\Rightarrow a^2+\dfrac{1}{a^2}=\left(a+\dfrac{1}a\right)^2-2=8^2-2=64-2=62,\ deci\ \boxed{a^2+\dfrac1{a^2}=62}.[/tex]

Ai înțeles rezolvarea ?

Green eyes.

[tex]a + \frac{1}{a} = 8 ridicam \: la \: patrat \\ (a + \frac{1}{a} ) {}^{2} = 8 {}^{2} \\ a {}^{2} + 2 \times a \times \frac{1}{a} + ( \frac{1}{a} ) {}^{2} = 64 \\ a {}^{2} + \frac{2a}{a} + \frac{1}{a {}^{2} } = 64 \\ a {}^{2} + 2 + \frac{1}{a {}^{2} } = 64 \\ a {}^{2} + \frac{1}{a {}^{2} } = 62[/tex]