Question

Ex 18 multumesc (troll=spamm de reporturi)

Answer 1

Explicație pas cu pas:

$\underbrace{\sqrt{ {(x - 2 \sqrt{2} )}^{2} }}_{ \geqslant 0} + \underbrace{\sqrt{ {(y - 3 \sqrt{2} )}^{2} }}_{ \geqslant 0} \leqslant 0$

$x - 2 \sqrt{2} = 0 \implies x = 2 \sqrt{2} \\ y - 3 \sqrt{2} = 0 \implies y = 3 \sqrt{2}$

=>

$m_{a} = \dfrac{x + y}{2} = \dfrac{2 \sqrt{2} + 3 \sqrt{2} }{2} = \dfrac{5 \sqrt{2} }{2}$

$m_{g} = \sqrt{xy} = \sqrt{2 \sqrt{2} \cdot 3 \sqrt{2} } = \sqrt{12} = 2 \sqrt{3}$

$m_{h} = \dfrac{2xy}{x + y} = \dfrac{2 \cdot 2 \sqrt{2} \cdot 3 \sqrt{2} }{2 \sqrt{2} + 3 \sqrt{2} } = \dfrac{24}{5 \sqrt{2} } = \dfrac{24 \sqrt{2} }{10} = \dfrac{12 \sqrt{2} }{5}$