Răspuns :
Răspuns
Media aritmetica inseamna suma tuturor termenilor impartit la numarul de termeni.
Media geometrica inseamna radacina patrata a tuturor elementelor
Adica radical din a*b*c*...n
Explicație pas cu pas:
Pentru 6,54
Ma= 60/2=30
Mg= radical 6x54 = radical 324=18
18<=30 (ADEVARAT)
Mg<=Ma
Pentru 1/4 si 1/9
Ma= (1/4+1/9)/2
Amplificam 1/4 cu 9 si 1/9 cu 4 si obtinem
(13/36)/2=1/6
Mg = radical 1/4* 1/9 = radical 1/36 = 1/6
1/6<=1/6(ADEVARAT)
Mg<=Ma
Pentru 28 radical 3 si 12 radical 3
Ma= (28 radical 3 + 12 radical 3)/2= 20 radical 3 = radical din 1200
Mg = radical din 28 radical 3 * 12 radical 3 = radical din 1008
Radical din 1008 <= radical 1200 ( ADEVAARAT)
Mg<=Ma
Restul le faci si tu, sa intelegi ceva :D succes. Sper ca n-am gresit pe undeva, ma grabesc ca o sa ma culc :D
a.
[tex] \sqrt{6 \times 54} < \frac{54 + 6}{2} \\ \\ \sqrt{324} < \frac{60}{2} \\ 18 < 30[/tex]
b.
[tex] \sqrt{ \frac{1}{4} \times \frac{1}{9} } < \frac{ \frac{1}{4} + \frac{1}{9} }{2} \\ \sqrt{ \frac{1}{36} } < \frac{ \frac{9}{36} + \frac{4}{36} }{2} \\ \frac{1}{6} < \frac{ \frac{13}{36} }{2} \\ \frac{1}{6} < \frac{13}{72} \\ \frac{1}{6} < \frac{1}{72} + \frac{12}{72} \\ \frac{1}{6} < \frac{1}{72} + \frac{1}{6} [/tex]
[tex] \sqrt{6 \times 54} < \frac{54 + 6}{2} \\ \\ \sqrt{324} < \frac{60}{2} \\ 18 < 30[/tex]
b.
[tex] \sqrt{ \frac{1}{4} \times \frac{1}{9} } < \frac{ \frac{1}{4} + \frac{1}{9} }{2} \\ \sqrt{ \frac{1}{36} } < \frac{ \frac{9}{36} + \frac{4}{36} }{2} \\ \frac{1}{6} < \frac{ \frac{13}{36} }{2} \\ \frac{1}{6} < \frac{13}{72} \\ \frac{1}{6} < \frac{1}{72} + \frac{12}{72} \\ \frac{1}{6} < \frac{1}{72} + \frac{1}{6} [/tex]