X^(1/2) + x^(-1/2) = 3, calcule
(x^(3/2) + x^(-3/2) + 2)
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(x^2 + x^-2 + 3)
(x^(3/2) + x^(-3/2) + 2)
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(x^2 + x^-2 + 3)
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√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