شاه کلید نکات
شاه کلید سوال
1 جزء صحیح اعداد زیر را به دست آورید و در صورت نیاز از محور اعداد، استفاده کنید.
\(\begin{array}{l}\left[ { - 3/4} \right] = \\\left[ { - 2} \right] = \\\left[ { - 1/1} \right] = \\\left[ {0/4} \right] = \\\left[ { - 0/4} \right] = \\\left[ {4/25} \right] = \\\left[ {\frac{{41}}{{37}}} \right] = \\\left[ {2/3} \right] = \\\left[ {1/7} \right] = \\\left[ { - \frac{{13}}{{51}}} \right] = \end{array}\)
\(\begin{array}{l}\left[ { - 3/4} \right] = - \;4\\\left[ { - 2} \right] = - \;2\\\left[ { - 1/1} \right] = - \;2\\\left[ {0/4} \right] = 0\\\left[ { - 0/4} \right] = - \;1\\\left[ {4/25} \right] = 4\\\left[ {\frac{{41}}{{37}}} \right] = \left[ {1\frac{6}{{37}}} \right] = 1\\\left[ {2/3} \right] = 2\\\left[ {1/7} \right] = 1\\\left[ { - \frac{{13}}{{51}}} \right] = - \;1\end{array}\)
2 حاصل \(\left[ 1 \right] + \left[ {\sqrt 2 } \right] + \left[ {\sqrt 3 } \right] + ... + \left[ {\sqrt {10} } \right]\) را به دست آورید.
\(\begin{array}{l}\left[ 1 \right] + \left[ {\sqrt 2 } \right] + \left[ {\sqrt 3 } \right] + ... + \left[ {\sqrt {10} } \right] = \\\\\left[ 1 \right] = 1\\\\1 < \sqrt 2 < 2 \Rightarrow \left[ {\sqrt 2 } \right] = 1\\\\1 < \sqrt 3 < 2 \Rightarrow \left[ {\sqrt 3 } \right] = 1\\\\\left[ {\sqrt 4 } \right] = \left[ 2 \right] = 2\\\\2 < \sqrt 5 < 3 \Rightarrow \left[ {\sqrt 5 } \right] = 2\\\\2 < \sqrt 6 < 3 \Rightarrow \left[ {\sqrt 6 } \right] = 2\\\\2 < \sqrt 7 < 3 \Rightarrow \left[ {\sqrt 7 } \right] = 2\\\\2 < \sqrt 8 < 3 \Rightarrow \left[ {\sqrt 8 } \right] = 2\\\\\left[ {\sqrt 9 } \right] = \left[ 3 \right] = 3\\\\3 < \sqrt {10} < 4 \Rightarrow \left[ {\sqrt {10} } \right] = 3\\\\\left[ 1 \right] + \left[ {\sqrt 2 } \right] + \left[ {\sqrt 3 } \right] + ... + \left[ {\sqrt {10} } \right] = \\\\1 + 1 + 1 + 2 + 2 + 2 + 2 + 2 + 3 + 3 = \\\\19\end{array}\)
3 حاصل \(\left[ x \right] + \left[ {2x} \right] + \left[ {3x} \right]\) را به ازای \(x = - \frac{5}{3}\) دست آورید.
\(\begin{array}{l}\left[ x \right] + \left[ {2x} \right] + \left[ {3x} \right] = \\\\ [ - \frac{5}{3}] + [2 \times ( - \frac{5}{3})] + [3 \times ( - \frac{5}{3})] = \\\\ [ - \frac{5}{3}] + [ - \frac{{10}}{3}] + [ - \frac{{15}}{3}] = \\\\( - 2) + ( - 4) + ( - 5) = - 11\end{array}\)
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