Question

Calculati media aritmetica a nr a si b unde :

A. a = 6 radical 3 + radical 108 - 4 radical 75 + 2 radical 147 =
b = 8 radical 3 + 33 radical 12 - 5 radical 27 =

Ma = a + b / 2

B . a = 3 radical 2 + 11 radical 7 - 2 radical 112 - radical 200 =
b = 3 radical 28 + 2 radical 63 - radical 252 - radical 175 =

Ma =

C. a = 22 radical 7 - radical 648 - radical 567 + 2 radical 162 =
b = 3 radical 567 - radical 800 + 2 radical 200 + 10 radical 175 =

Ma =



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Answer 1

$\displaystyle 1).a=6 \sqrt{3} + \sqrt{108} -4 \sqrt{75} +2 \sqrt{147} \\ a=6 \sqrt{3} +6 \sqrt{3} -4 \cdot 5 \sqrt{3} +2 \cdot 7 \sqrt{3} \\ a=6 \sqrt{3} +6 \sqrt{3} -20 \sqrt{3} +14 \sqrt{3} \\ a=6 \sqrt{3} \\ b=8 \sqrt{3} +33 \sqrt{12} -5 \sqrt{27} \\ b=8 \sqrt{3} +33 \cdot 2 \sqrt{3} -5 \cdot 3 \sqrt{3} \\ b=8 \sqrt{3} +66 \sqrt{3} -15 \sqrt{3} \\ b=59 \sqrt{3} \\ \\ m_a= \frac{6 \sqrt{3} +59 \sqrt{3} }{2} = \frac{65 \sqrt{3} }{2}$

$\displaystyle 2).a=3 \sqrt{2} +11 \sqrt{7} -2 \sqrt{112} - \sqrt{200} \\ a=3 \sqrt{2} +11 \sqrt{7} -2 \cdot 4 \sqrt{7} -10 \sqrt{2} \\ a=3 \sqrt{2} +11 \sqrt{7} -8 \sqrt{7} -10 \sqrt{2} \\ a=-7 \sqrt{2} +3 \sqrt{7} \\ b=3 \sqrt{28} +2 \sqrt{63} - \sqrt{252} - \sqrt{175} \\ b= 3 \cdot 2 \sqrt{7} +2 \cdot 3 \sqrt{7} -6 \sqrt{7} -5 \sqrt{7} \\ b=6 \sqrt{7} +6 \sqrt{7} -6 \sqrt{7} -5 \sqrt{7} \\ b= \sqrt{7} \\ \\ m_a= \frac{-7 \sqrt{2} +3 \sqrt{7} + \sqrt{7} }{2} = \frac{-7 \sqrt{2} +4 \sqrt{7} }{2}$

$\displaystyle 3).a=22 \sqrt{7} - \sqrt{648} - \sqrt{567} +2 \sqrt{162} \\ a=22 \sqrt{7} -18 \sqrt{2} -9 \sqrt{7} +2 \cdot 9 \sqrt{2} \\ a=22 \sqrt{7} -18 \sqrt{2} -9 \sqrt{7} +18 \sqrt{2} \\ a=13 \sqrt{7} \\ b=3 \sqrt{567} - \sqrt{800} +2 \sqrt{200} +10 \sqrt{175} \\ b=3 \cdot 9 \sqrt{7} -20 \sqrt{2} +2 \cdot 10 \sqrt{2} +10 \cdot 5 \sqrt{7} \\ b=27 \sqrt{7} -20 \sqrt{2} +20 \sqrt{2} +50 \sqrt{7} \\ b=77 \sqrt{7} \\ \\ m_a= \frac{13 \sqrt{7}+77 \sqrt{7} }{2} = \frac{90 \sqrt{7} }{2} =45 \sqrt{7}$