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Solve for `x:2^(x+2) gt (1/4)^(1/x)`

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Solve for `x:2^(x+2) gt (1/4)^(1/x)`
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We have `2^(x+2) gt 2^(-2//x)`. Since the base `2 gt 1`, we have `x +2 gt -2/x`
(the sign of the inequality is retained).
Now `x+2+2/x gt 0 rArr (x^(2)+2x+2)/(x) gt 0`
`rArr ((x+1)^(2)+1)/(x) gt sqrt(x) rArr x in (0,infty)`
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