Răspuns:
a) [tex]a=2\sqrt{2} [/tex]
b) [tex]media = \frac{5\sqrt{2} }{2} [/tex]
Explicație pas cu pas:
a)
[tex]a=\sqrt{6} (\frac{3}{\sqrt{2} } +\frac{2}{\sqrt{3} } )-\sqrt{27} [/tex]
[tex]a=\sqrt{2} *\sqrt{3} (\frac{3\sqrt{3}+2\sqrt{2} }{\sqrt{2}*\sqrt{3} }) - \sqrt{9*3} [/tex]
[tex]a=3\sqrt{3} + 2\sqrt{2} - 3\sqrt{3} [/tex]
[tex]a=2\sqrt{2} [/tex]
b) Inainte de a calcula media, il prelucram putin pe b
[tex]b=\sqrt{12} + \sqrt{18} -2\sqrt{3} [/tex]
[tex]b=\sqrt{4*3} + \sqrt{9*2} - 2\sqrt{3} [/tex]
[tex]b=2\sqrt{3} + 3\sqrt{2} -2\sqrt{3} [/tex]
[tex]b = 3\sqrt{2} [/tex]
Acum calculam media aritmetica:
[tex]\frac{a+b}{2} = \frac{2\sqrt{2}+3\sqrt{2} }{2} = \frac{5\sqrt{2} }{2} [/tex]
