Question

A) Sa se arate ca a=2 radical 2
B) Calculati media aritmetica a numerelor a si b

Answer 1

Răspuns:

a) $a=2\sqrt{2}$

b) $media = \frac{5\sqrt{2} }{2}$

Explicație pas cu pas:

a)

$a=\sqrt{6} (\frac{3}{\sqrt{2} } +\frac{2}{\sqrt{3} } )-\sqrt{27}$

$a=\sqrt{2} *\sqrt{3} (\frac{3\sqrt{3}+2\sqrt{2} }{\sqrt{2}*\sqrt{3} }) - \sqrt{9*3}$

$a=3\sqrt{3} + 2\sqrt{2} - 3\sqrt{3}$

$a=2\sqrt{2}$

b) Inainte de a calcula media, il prelucram putin pe b

$b=\sqrt{12} + \sqrt{18} -2\sqrt{3}$

$b=\sqrt{4*3} + \sqrt{9*2} - 2\sqrt{3}$

$b=2\sqrt{3} + 3\sqrt{2} -2\sqrt{3}$

$b = 3\sqrt{2}$

Acum calculam media aritmetica:

$\frac{a+b}{2} = \frac{2\sqrt{2}+3\sqrt{2} }{2} = \frac{5\sqrt{2} }{2}$