4 Calculați media geometrică a numerelor a și b:
a = V12-2727 +53+48 +2775,
b = V(5 - 13) - V(213 - 313)? – V(5-3/2)2 +172 – 12.
+

a=2√3-3√3+5√3+4√3+10√3=18√3

b=(5-√3)-(2√3-3√2)-(5-3√2)+7-1=5-√3-(3√2-2√3)-5+3√2+6=5-√3-3√2+2√3-5+3√2+6=6+√3

M²=a*b=18√3(6+√3)=108√3+54=54(2√3+1)

M=√[54(2√3+1)]=3√[6(2√3+1)]

Răspuns:

[tex]m_g=15[/tex]

Explicație pas cu pas:

[tex]a=\sqrt{12} -2\sqrt{27} +5\sqrt{3} +\sqrt{48} +2\sqrt{75}[/tex]

[tex]a=2\sqrt{3} -2*3\sqrt{3} +5\sqrt{3} +4\sqrt{3} +2*5\sqrt{3}[/tex]

[tex]a=2\sqrt{3} -6\sqrt{3} +5\sqrt{3} +4\sqrt{3} +10\sqrt{3}[/tex]

[tex]a=-4\sqrt{3} +5\sqrt{3} +4\sqrt{3} +10\sqrt{3}[/tex]

[tex]a=\sqrt{3} +4\sqrt{3} +10\sqrt{3}[/tex]

[tex]a=5\sqrt{3} +10\sqrt{3}[/tex]

[tex]a=15\sqrt{3}[/tex]

[tex]b=\sqrt{(5-\sqrt{3})^2 } -\sqrt{(2\sqrt{3}-3\sqrt{2} )^2 } -\sqrt{(5-3\sqrt{2})^2 } +\sqrt{7^2-1^2}[/tex]

[tex]b=5-\sqrt{3} -|2\sqrt{3} -3\sqrt{2} |-(5-3\sqrt{2} )+\sqrt{49-1}[/tex]

[tex]b=5-\sqrt{3} -(3\sqrt{2} -2\sqrt{3} )-(5-3\sqrt{2} )+\sqrt{48}[/tex]

[tex]b=5-\sqrt{3} -3\sqrt{2}+2\sqrt{3} -5+3\sqrt{2} +4\sqrt{3}[/tex]

[tex]b=-\sqrt{3} -3\sqrt{2} +2\sqrt{3} +3\sqrt{2} +4\sqrt{3}[/tex]

[tex]b=-\sqrt{3} +2\sqrt{3} +4\sqrt{3}[/tex]

[tex]b=\sqrt{3} +4\sqrt{3}[/tex]

[tex]b=5\sqrt{3}[/tex]

[tex]m_g=\sqrt{a*b} =\sqrt{15\sqrt{3}*5\sqrt{3} }[/tex]

[tex]m_g=\sqrt{15*3*5} =\sqrt{225}[/tex]

[tex]m_g=15[/tex]