Question

Ex 20 multumesc (troll=spamm de reporturi)

Answer 1

Răspuns:

Explicație pas cu pas:

Answer 2

Explicație pas cu pas:

a)

$- 2 \sqrt{5} - 4 < 0 \implies | - 2 \sqrt{5} - 4| = - (- 2 \sqrt{5} - 4) = 2 \sqrt{5} + 4$

$\implies a = | - 2 \sqrt{5} - 4| = 2 \sqrt{5} + 4$

$4 - 2 \sqrt{5} = \sqrt{16} - \sqrt{20} < 0 \\ \implies |4 - 2 \sqrt{5}| = - (4 - 2 \sqrt{5}) = 2 \sqrt{5} - 4$

$b = \sqrt{ {(4 - 2 \sqrt{5})}^{2} } = |4 - 2 \sqrt{5}| = 2 \sqrt{5} - 4$

=>

$2 \sqrt{5} + 4 > 2 \sqrt{5} - 4 \implies \bf a > b$

b)

$m_{p} = \dfrac{p_{1} \cdot a + p_{2} \cdot b}{p_{1} + p_{2}} = \dfrac{3 \cdot (2 \sqrt{5} + 4) + 5 \cdot (2 \sqrt{5} - 4)}{3 + 5} =$

$= \dfrac{6 \sqrt{5} + 12 + 10 \sqrt{5} - 20}{8} = \dfrac{16 \sqrt{5} - 8}{8}$

$= \dfrac{8(2 \sqrt{5} - 1)}{8} = \bf 2 \sqrt{5} - 1$