Prove that the geometric mean of two real numbers a and b, is greater than or equal to the harmonic mean of a and b.

Note that the inequality is only true when a and b are both the same sign (because the geometric mean requires a×b to be positive).

This allows us to take the square root of the inequality in step 6 without worrying about a negative radicand.

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Do you need with the x value for the minimum? its always between the two intercepts for a parabola