Question

Ex 23 multumesc(troll=spamm de reporturi)

Answer 1

Explicație pas cu pas:

inegalitatea mediilor:

$\sqrt{2x} = \sqrt{1 \cdot 2x} \leqslant \dfrac{1 + 2x}{2}$

$\sqrt{2x + 4} = \sqrt{1 \cdot (2x + 4)} \leqslant \dfrac{1 + 2x + 4}{2} = \dfrac{2x + 5}{2}$

$\sqrt{2x + 5} = \sqrt{1 \cdot (2x + 5)} \leqslant \dfrac{1 + 2x + 5}{2} = \dfrac{2x + 6}{2}$

=>

$\sqrt{2x} + \sqrt{2x + 4} + \sqrt{2x + 5} \leqslant \dfrac{2x + 1 + 2x + 5 + 2x + 6}{2} = \dfrac{6x + 12}{2} = \dfrac{2(3x + 6)}{2} = 3x + 6$

=>

$\sqrt{2x} + \sqrt{2x + 4} + \sqrt{2x + 5} \leqslant 3x + 6$

q.e.d.