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Problem Solving (PS) | The value of (1/x)-(4/√x)+4 is least when x =

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Can someone explain this in a bit more detail? The approach seems really advanced and is not something I would arrive logically.
What am I missing Image

I had a approach where I just plugged in numbers and it was clear that it has to be either 1 / sqrt (6) or 1 / 4
From here it got a bit messy.

But I estimated sqrt 6 as 2.50 and with
...

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