Question

preciso de uma resposta detalhada

Answer 1

Resposta:

Explicação passo-a-passo:

$a^{\frac{1}{2}}+a^{\frac{-1}{2}}=\frac{10}{3}\\elevando \ ambos \ os \ lados \ ao \ quadrado \\\\(a^{\frac{1}{2}}+a^{\frac{-1}{2}})^2=(\frac{10}{3})^2\\\\(a+b)^2=a^2+2ab+b^2\\(a^{\frac{1}{2}})^2+2*a^{\frac{1}{2}}*a^{-\frac{1}{2}}=\frac{100}{9}\\\\sabemos \ que\\a^n*a^m= a^{n+m} \ entao\\a^{\frac{1}{2}}*a^{-\frac{1}{2}}= a^{\frac{1}{2}+(-\frac{1}{2})}=a^0=1\\\\continuando\\\\(a^b)^n= a^{bn}\\(a^{\frac{1}{2}})^2= a^{\frac{2}{2}}= a^1=a\\analogamente \ para \ (a^{-\frac{1}{2}})^2 =a^{-1}$

$a+2+a^{-1}=\frac{100}{9}\\a+a^{-1}=\frac{100}{9}-2\\a+a^{-1}=\frac{82}{9}$