Question

Calculați media aritmetica si geometrica :
$a) \sqrt{(5 + 3 \sqrt{3} } {}^{2}$
$b) |5 - 3 \sqrt{3} |$
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Answer 1

a = 5 + 3 radical 3

b = 3 radical 3 - 5

M.a.( a,b) = (5 + 3 radical 3 + 3 radical 3 - 5) : 2 = 6 radical 3 : 2 = 3 radical 3

M.g.(a,b) = radical ([3 radical 3 + 5)*(3 radical 3 - 5)] = radical[(3 radical 3)^2 - 5^2] = radical (9*3-25) = radical 2