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Calculati media aritmetica si geometrica:

a)
[tex]x = \sqrt{7} - 2 \\ y = \sqrt{7} + 2[/tex]
b)
[tex]x = \sqrt{11} - \sqrt{3} \\ y = \sqrt{11} + \sqrt{3} [/tex]
c)
[tex]x = 9 - 4 \sqrt{2} \\ y = 4 \sqrt{2} + 9[/tex]
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Dau coroana​


Răspuns :

Media aritmetica: ma=[tex]\frac{x+y}{2}[/tex]

[tex]m_a=\frac{\sqrt{7} -2+\sqrt{7}+2 }{2} =\frac{2\sqrt{7} }{2} =\sqrt{7} \\~m_a=\frac{\sqrt{11}-\sqrt{3}+\sqrt{11}+\sqrt{3}}{2} =\frac{2\sqrt{11} }{2} =\sqrt{11}\\ ~m_a=\frac{9-4\sqrt{2}+4\sqrt{2}+9}{2} =\frac{18}{2}=9[/tex]

Media geometrica : [tex]m_g=\sqrt{x*y}\\m_g=\sqrt{(\sqrt{7}-2)(\sqrt{7}+2)}=\sqrt{7-4}=\sqrt{3}\\m_g=\sqrt{(\sqrt{11}-\sqrt{3})(\sqrt{11}+\sqrt{3)}}=\sqrt{11-3}=2\sqrt{2}\\m_g=\sqrt{(9+4\sqrt{2})(9-4\sqrt{2)}}=\sqrt{81-32}=\sqrt{49}=7[/tex]