Răspuns:
[tex]\frac{x+y}{2} = 2\sqrt{7} - \frac{7\sqrt{2} }{2}[/tex]
Explicație pas cu pas:
[tex]x = 2\sqrt{63} - \sqrt{252} +3\sqrt{28} - \sqrt{175}[/tex]
[tex]x = 2\sqrt{9*7} - \sqrt{36*7} + 3\sqrt{4*7} - \sqrt{25*7}[/tex]
[tex]x = 2*3\sqrt{7} - 6\sqrt{7} + 3*2\sqrt{7} - 5\sqrt{7}[/tex]
[tex]x = 6\sqrt{7} - 6\sqrt{7} + 6\sqrt{7} - 5\sqrt{7}[/tex]
[tex]x = \sqrt{7}[/tex]
[tex]y = \sqrt{18} + \sqrt{847} - 2\sqrt{112} - 5\sqrt{8}[/tex]
[tex]y = \sqrt{9*2} + \sqrt{121*7} - 2\sqrt{16*7} - 5\sqrt{4*2}[/tex]
[tex]y = 3\sqrt{2} + 11\sqrt{7} - 2*4\sqrt{7} - 5*2\sqrt{2}[/tex]
[tex]y = 3\sqrt{2} + 11\sqrt{7} - 8\sqrt{7} - 10\sqrt{2}[/tex]
[tex]y = 3\sqrt{7} - 7\sqrt{2}[/tex]
[tex]\frac{x+y}{2} = \frac{\sqrt{7} + 3\sqrt{7} - 7\sqrt{2} }{2} = \frac{4\sqrt{7} - 7\sqrt{2} }{2} = 2\sqrt{7} - \frac{7\sqrt{2} }{2}[/tex]
Aducem numerele la o formă mai simplă:
[tex]x = 2\sqrt{63} - \sqrt{252} + 3\sqrt{28} - \sqrt{175} =\\[/tex]
[tex]= 2\sqrt{3^2 \cdot7} - \sqrt{6^2\cdot7} + 3\sqrt{2^2\cdot7} - \sqrt{5^2\cdot7}\\[/tex]
[tex]= 2 \cdot 3\sqrt{7} - 6\sqrt{7} + 3 \cdot 2\sqrt{7} - 5\sqrt{7}[/tex]
[tex]= 6\sqrt{7} - 6\sqrt{7} + 6\sqrt{7} - 5\sqrt{7} = \bf \sqrt{7}[/tex]
[tex]y = \sqrt{18} + \sqrt{847} - 2\sqrt{112} - 5\sqrt{8}=\\[/tex]
[tex]= \sqrt{2 \cdot 3^2} + \sqrt{7 \cdot 11^2} - 2\sqrt{4^2 \cdot 7} - 5\sqrt{2^2 \cdot 2}\\[/tex]
[tex]= 3\sqrt{2} + 11\sqrt{7} - 2\cdot4\sqrt{7} - 5\cdot2\sqrt{2}\\[/tex]
[tex]= 3\sqrt{2} + 11\sqrt{7} - 8\sqrt{7} - 10\sqrt{2}\\[/tex]
[tex]= \bf3\sqrt{7} - 7\sqrt{2}\\[/tex]
Media aritmetică este:
[tex]m_a = \dfrac{x+y}{2} = \dfrac{\sqrt{7} + 3\sqrt{7} - 7\sqrt{2}}{2} = \dfrac{4\sqrt{7} - 7\sqrt{2}}{2}[/tex]
