My age is (a!-2a); where a is the minimum value of x+ $\frac{4}{x}$ . How old am I?

15
14
20
21
16
18
19
17

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$Let~ y=x+\dfrac{4}{x}.~~$ Differentiating and equating to zero we get x = 2 or -2. Since factorials are for + tive integers, we have $\\a = 2 + \dfrac{4}{2} = 4. \\So~ (a!-2a) =~~ (4!-2*4) ~~= (24-8) = 16$