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Verde6106
Pe: 2015-09-20T17:50:44+03:00 In: In:

Ajutor matematica clasa a 9a

Nu zice exact ce trebuie sa fac , dar probabil trebuie sa demontrez aceasta inegalitate.Intr-o paranteza zice ca este ,, Inegalitatea lui Minkowski”. Va multumesc anticipat! +

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4 raspunsuri

  1. alex05ok
  2. alex05ok
  4. alex05ok
  5. gunty
    maestru (V)

        \[ \begin{array}{l} \sqrt {\left( {a + b} \right)^2 + \left( {x + y} \right)^2 } \le \sqrt {a^2 + x^2 } + \sqrt {b^2 + y^2 } \\ \Leftrightarrow a^2 + b^2 + 2ab + x^2 + y^2 + 2xy \le a^2 + x^2 + b^2 + y^2 + 2\sqrt {a^2 + x^2 } \cdot \sqrt {b^2 + y^2 } \\ \Leftrightarrow 2ab + 2xy \le 2\sqrt {\left( {a^2 + x^2 } \right)\left( {b^2 + y^2 } \right)} \\ \Leftrightarrow ab + xy \le \sqrt {a^2 b^2 + a^2 y^2 + b^2 x^2 + x^2 y^2 } \quad ...\left( * \right) \\ \end{array} \]

        \[ Daca\;ab + xy < 0,\;atunci\;inegalitatea\;\left( * \right)\;este\;evident\;adevarata. \]

    *** QuickLaTeX cannot compile formula:
\[
	\begin{array}{l}
	 Daca\;ab + xy \ge 0]

*** Error message:
\begin{array} on input line 9 ended by \end{document}.
leading text: \end{document}
Improper \prevdepth.
leading text: \end{document}
Missing $ inserted.
leading text: \end{document}
Missing } inserted.
leading text: \end{document}
Missing \cr inserted.
leading text: \end{document}
Missing $ inserted.
leading text: \end{document}
You can't use `\end' in internal vertical mode.
leading text: \end{document}
\begin{array} on input line 9 ended by \end{document}.
leading text: \end{document}
Missing } inserted.
leading text: \end{document}
Emergency stop.

    Astfel inegalitatea din enunt este demonstrata 🙂.

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