[tex] \sqrt{17-4 \sqrt{9+4 \sqrt{5} } } = \sqrt{5} -2[/tex] | ridicam la patrat
[tex]17-4 \sqrt{9+4 \sqrt{5} } =9-4 \sqrt{5} [/tex]
[tex]8-4 \sqrt{9+ \sqrt{80} } =-4 \sqrt{5} [/tex] impartim cu 4
[tex]2- \sqrt{9+ \sqrt{80} } =- \sqrt{5} [/tex]
Folosim formula radicalilor compusi!!! ______________
[tex] \sqrt{a+ \sqrt{b} } = \sqrt{ \frac{a+ \sqrt{a^2-b} }{2} } +\sqrt{ \frac{a- \sqrt{a^2-b} }{2} }[/tex]
[tex] \sqrt{9+ \sqrt{80} } = \sqrt{ \frac{9+ \sqrt{81-80} }{2} } +\sqrt{ \frac{9- \sqrt{81-80} }{2} } [/tex]
[tex] \sqrt{5} + \sqrt{4} [/tex]
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[tex]2- \sqrt{5} - \sqrt{4} =- \sqrt{5} [/tex]
Se reduce tot , 0=0(A)
[tex]b) \frac{1}{ \sqrt{2} +1}+...+ \frac{1}{ \sqrt{100}+ \sqrt{99} } =9[/tex]
Amplificam cu conjugata:
[tex] \frac{ \sqrt{2}-1 }{2-1} + \frac{ \sqrt{3}- \sqrt{2} }{3-2} +...+ \frac{ \sqrt{100}- \sqrt{99} }{100-99} [/tex]
[tex] \sqrt{2} -1+ \sqrt{3}- \sqrt{2} +...+ \sqrt{99}- \sqrt{98} + \sqrt{100} - \sqrt{99} [/tex]
Se duce tot, inafara de -1 si 10 , care adunate dau exact 9.
c) proprietatea log: b(log in baza b din x) =x
36 la (log baza 6 din 5)=6 la(log baza 6 din 5) ori 6 la( log baza 6 din 5)
=5*5=25. (uita-te in atasament sau http://prntscr.com/5a3v50
