Question

x^(1/2) + x^(-1/2) = 3, calcule 

(x^(3/2) + x^(-3/2) + 2)
-----------------------------
   (x^2 + x^-2 + 3)

Answer 1

Boa tarde Mozarth

√x + 1/√x = 3 

(√x + 1/√x)³ = 27

√x³ + 1/√x³ + 3*(√x + 1/√x) = 27
√x³ + 1/√x³ = 27 - 9 = 18

(√x + 1/√x)² = (x + 2 + 1/x) = 9
x + 1/x = 7

(√x + 1/√x)⁴ = 81

x² + 1/x² + 4*(x + 1/x) + 6 = 81
x² + 1/x² + 4*7 + 6 = 81
x² + 1/x² = 81 - 34 = 47

E = (18 + 2)/(47 + 3) = 20/50 = 2/5