Question

mai am nevoie doar de a,f,h.va rog repedeee​

Answer 1

Explicație pas cu pas:

$m_{h} \leqslant m_{g} \leqslant m_{a}$

$\dfrac{2ab}{a + b} \leqslant \sqrt{ab} \leqslant \dfrac{a + b}{2}$

a)

$m_{h} = \dfrac{2 \cdot 6 \cdot 54}{6 + 54} = \dfrac{648}{60} = \dfrac{54}{5} = 10 \frac{4}{5}$

$m_{g} = \sqrt{6 \cdot 54} = \sqrt{ {3}^{2} \cdot {6}^{2} } = 18$

$m_{a} = \dfrac{6 + 54}{2} = \dfrac{60}{2} = 30$

$10 \dfrac{4}{5} \leqslant 18 \leqslant 30 \implies m_{h} \leqslant m_{g} \leqslant m_{a}$

b)

$m_{h} = \dfrac{2 \cdot \dfrac{6}{5} \cdot \dfrac{24}{25} }{\dfrac{6}{5} + \dfrac{24}{25}} = \dfrac{\dfrac{288}{125} }{\dfrac{150 + 120}{125}} = \dfrac{288}{270} = \dfrac{16}{15}$

$m_{g} = \sqrt{\dfrac{6}{5} \cdot \dfrac{24}{25}} = \sqrt{\dfrac{144}{125}} = \dfrac{12}{5 \sqrt{5} } = \dfrac{12 \sqrt{5} }{25}$

$m_{a} = \dfrac{\dfrac{6}{5} + \dfrac{24}{25}}{2} = \dfrac{\dfrac{270}{125}}{2} = \dfrac{270}{250} = \dfrac{27}{25}$

$\dfrac{16}{15} = \sqrt{ \dfrac{256}{225} } < \sqrt{\dfrac{144}{125}} < \sqrt{\dfrac{729}{625}} = \dfrac{27}{25}$

$\implies m_{h} \leqslant m_{g} \leqslant m_{a}$