Question: Please solve 9 9. If a and b are two positive numbers, the numbers mA, mc, and my defined by MA = - (a+ b).

Please solve 9

9. If a and b are two positive numbers, the numbers mA, mc, and my defined by MA = - (a+ b). mc = vab, and + MH SECTION 1.7 / INTERVALS AND ABSOLUTE VALUES 29 are called the arithmetic, geometric, and harmonic means of a and b. Prove that MA > MG 2 MH with strict inequalities unless a = b. (Hint: You should first test these inequalities by choosing some specific numbers, using a calculator if you wish. To show that mA 2 mc, start with the obvious inequality (va-vb)' 2 0, and then expand. To show that my 2 my, start by showing that xy

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