A mathematical problem of filling in the blanks (basic inequality and its application) If x < 0, then x + 1 / X - 2 It's x + 1 / X () - 2

A mathematical problem of filling in the blanks (basic inequality and its application) If x < 0, then x + 1 / X - 2 It's x + 1 / X () - 2

Because x < 0, then - x > 0
So x + 1 / x = - [(- x) + (- 1 / x)]
Because [(- x) + (- 1 / x)] > = under 2 times root sign [(- x) (- 1 / x)]
=2
So [(- x) + (- 1 / x)] > = 2
Therefore - [(- x) + (- 1 / x)] < = - 2