Ecuatie radical la puterea x

Elena09 Sam Iun 02, 2012 2:33 pm

Sa se rezolve ecuatia: $(\sqrt{3+2\sqrt{2}})^x + (\sqrt{3-2\sqrt{2}})^x=6$

**Admin** Sam Iun 02, 2012 9:16 pm

$\begin{array}{l} {\left( {\sqrt {3 + 2\sqrt 2 } } \right)^x} + {\left( {\sqrt {3 - 2\sqrt 2 } } \right)^x} = 6\left| { \times {{\left( {\sqrt {3 - 2\sqrt 2 } } \right)}^x}} \right. \Rightarrow \underbrace {{{\left( {\sqrt {3 + 2\sqrt 2 } } \right)}^x} \times {{\left( {\sqrt {3 - 2\sqrt 2 } } \right)}^x}}_{ = 1} + {\left( {\sqrt {3 - 2\sqrt 2 } } \right)^{2x}}\\ = 6{\left( {\sqrt {3 - 2\sqrt 2 } } \right)^x}\\ {\rm{Notam}}:{\left( {\sqrt {3 - 2\sqrt 2 } } \right)^x} = y \Rightarrow {y^2} + 1 = 6y \Rightarrow {y_{1,2}} = 3 \pm 2\sqrt 2 \Rightarrow {\left( {\sqrt {3 - 2\sqrt 2 } } \right)^x} = 3 \pm 2\sqrt 2 \Rightarrow x = ... \end{array}$

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Lauryca Dum Iun 03, 2012 5:05 pm

Nu.Am inteles-o perfect!

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Ecuatie radical la puterea x

Ecuatie radical la puterea x

Re: Ecuatie radical la puterea x

Perfect

Re: Ecuatie radical la puterea x