Răspuns:
Explicație pas cu pas:
Media aritmetica
ma = (a+b)/2
Media geometrica
mg=[tex]\sqrt{a*b}[/tex]
a) ma = (12+75)/2 = 87/2 = 43.5
mg = [tex]\sqrt{12*75} = \sqrt{900} = 30[/tex]
ma > mg
b) ma = [tex](6\sqrt2} + 3\sqrt2})/2 = 9\sqrt2} /2[/tex]
mg = [tex]\sqrt{6\sqrt{2} * 3\sqrt{2}} = \sqrt{18\sqrt{4}} = \sqrt{18*2}} = \sqrt{36} = 4[/tex]
ma > mg
c) ma = [tex](\sqrt5} + \sqrt5})/2 = 2\sqrt5} /2[/tex]
mg = [tex]\sqrt{\sqrt{5} * \sqrt{5}} = \sqrt{\sqrt{25}} = \sqrt{5}[/tex]
ma < mg
d) ma = (0.7+2.8)/2 = 3.5/2 = 1.75
mg = [tex]\sqrt{0.7*2.8} = \sqrt{1.96}} = 1.4\\[/tex]
ma > mg
e) ma = [tex](\sqrt50} + \sqrt2})/2 = (5\sqrt{2} } + \sqrt2})/2 = 6\sqrt2} /2 = 3\sqrt2}[/tex]
mg = [tex]\sqrt{\sqrt{50} * \sqrt{2}} = \sqrt{\sqrt{100}} = \sqrt{10}[/tex]
ma > mg
f) ma = [tex](3+\sqrt5} + 3-\sqrt5})/2 = 6/2 = 3[/tex]
mg = [tex]\sqrt{(3+\sqrt{5}) * (3-\sqrt{5})} = \sqrt{3^{2} - \sqrt{5^{2}}}= \sqrt {9 - 5}}}= \sqrt {4}}} = 2[/tex]
ma > mg
