Question

Se a^½ + a^½ = 3/10 então a + a-¹ vale:

a) 100/9

b) 82/3

c) 82/9

d) 100/82

e) 16/9​

Answer 1

Resposta:

Letra  c   :   82 / 9

Explicação passo-a-passo:

[a^1/2+a^-1/2]^2=[10/3]^2

$(a^{\dfrac{1}{2} }+\dfrac{1}{a^{\frac{1}{2} } }  )^{2} =\dfrac{10^{2} }{3^{2} } \Rightarrow a+2+\dfrac{1}{a} =\dfrac{100}{9}\Rightarrow a+a^{-1}  =\dfrac{100}{9} -2 \Rightarrow a+a^{-1}=\dfrac{82}{9}$