Question

Calculati media aritmetica si geometrica:

a)
$x = \sqrt{7} - 2 \\ y = \sqrt{7} + 2$
b)
$x = \sqrt{11} - \sqrt{3} \\ y = \sqrt{11} + \sqrt{3}$
c)
$x = 9 - 4 \sqrt{2} \\ y = 4 \sqrt{2} + 9$
Va rog mult sa ma ajutati
Dau coroana​

Answer 1

Sper ca intelegi. Succes!

Answer 2

Media aritmetica: ma=$\frac{x+y}{2}$

$m_a=\frac{\sqrt{7} -2+\sqrt{7}+2 }{2} =\frac{2\sqrt{7} }{2} =\sqrt{7} \\~m_a=\frac{\sqrt{11}-\sqrt{3}+\sqrt{11}+\sqrt{3}}{2} =\frac{2\sqrt{11} }{2} =\sqrt{11}\\ ~m_a=\frac{9-4\sqrt{2}+4\sqrt{2}+9}{2} =\frac{18}{2}=9$

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