Question

aflati media geometrica a numerelor:
a=radical mare 7-2radical din 6
b=radical mare 7+2radical din 6

Answer 1

a=√(7-2√6)=√(7-√24)=√[(7+√(49-24)]/2+√[(7-√(49-24)]/2=√(7+√25)/2+√(7-√25)/2=
=√(7+5)/2+√(7-5)/2=√12/2+√2/2=√6+1



b=√(7+2√6)=√(7+√24)=√[(7+√(49-24)]/2-√[(7-√(49-24)]/2=√(7+√25)/2-√(7-√25)/2=
=√(7+5)/2-√(7-5)/2=√12/2-√2/2=√6-1

Mg=√(√6+1)(√6-1)=√(6-1)=√5

Answer 2

[tex]m_g=\sqrt{a\cdot{b}}= ...\;\;\;\;\;\;a\cdot{b}=\sqrt{(7-2\sqrt6)(7+2\sqrt6)}=\sqrt{49-24}=5\;;\\ \Rightarrow\;m_g=\sqrt{a*b}=\sqrt5[/tex]