We know that the function

F(x+\(\frac{1}{x}\))=\(x^2 + \frac{1}{x^2}\)

To find F(4)\(x + \frac{1}{x}\) = 4

Squaring on both sides

\(x^2 + \frac{1}{x^2} + 2*x^2*\frac{1}{x^2}\) = 16

\(x^2 + \frac{1}{x^2}\) = 16-2 =14

To find F(5)\(x + \frac{1}{x}\) = 5

Squaring on both sides

\(x^2 + \frac{1}{x^2} + 2*x^2*\frac{1}{x^2}\) = 25

\(x^2 + \frac{1}{x^2}\) = 25-2 =23

So the sum of F(4) and F(5) = 14+23 = 37

(Option D)
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