Question

(3) Prove that AM >= GM >= HM for 2 variables.


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Answer 1

Am of a, b is a+b/2

GM of a, b=

$\ \sqrt{ab}$

HM of a, b=a+b/ab

${gm}^{2} = ab \\ 2am = a + b \\ hm = a+ b \div ab \\ hm = 2am \div {gm}^{2} \\ hm \times {gm}^{2} = 2am$