Question

stiind ca
$a - \frac{1}{a } = 3$
aratati ca
${a}^{2} + \frac{1}{ {a}^{2} } = 11$

Answer 1

a-1/a=3 si trebuie sa demonstram ca a^2+1/a^2=11
a-1/a=3
a^2-2a*1/a+1^2/a^2=3^2
a^2-2+1/a^2=9
a^2+1/a^2=9+2
a^2+1/a^2=11