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.

Question

Mathematics

Kade Riggs

11 July, 09:53

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.

+2

Answers (1)

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Kiera Mitchell · Answer 1

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.

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

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.