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</div></div><div align="center" class="tochead"><h1>23. FEJEZET: Négyzetgyök (teszt)</h1></div>
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<div class="feladat"><b>Feladat: 23.1.</b><br /> <a name="a_i_gyok_060520_HAFT_04_teszt_01" /><a href="bib_box.php?mode=sne---j-&amp;citation_num=" target="bib_box" onclick="mutat('bib_box.php?mode=sne---j-&amp;citation_num='); return false;"></a>Tekintsük az alábbi mennyiségeket!

<div class="p"><!----></div>

<m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>U</m:mi><m:mo>=</m:mo></m:mrow></m:math> az egységnyi élű kocka átlójának fele;

<div class="p"><!----></div>

<m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>V</m:mi><m:mo>=</m:mo></m:mrow></m:math> az egységnyi oldalú szabályos háromszög magassága;

<div class="p"><!----></div>

<m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>X</m:mi><m:mo>=</m:mo></m:mrow></m:math> annak a rombusznak a területe (egységnégyzetben), amelynek minden oldala egységnyi és van két <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow>

<m:msup><m:mrow><m:mn>120</m:mn></m:mrow><m:mrow><m:mo>&SmallCircle;</m:mo></m:mrow>

</m:msup>

</m:mrow></m:math>-os szöge; 

<div class="p"><!----></div>

<m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>Y</m:mi><m:mo>=</m:mo>

<m:mfrac><m:mrow><m:mn>3</m:mn></m:mrow>

<m:mrow><m:mn>2</m:mn><m:msqrt><m:mrow><m:mn>3</m:mn></m:mrow></m:msqrt></m:mrow>

</m:mfrac>

<m:mo>;</m:mo></m:mrow></m:math>

<div class="p"><!----></div>

<m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>Z</m:mi><m:mo>=</m:mo>

<m:mfrac><m:mrow><m:msqrt><m:mrow><m:mn>3</m:mn></m:mrow></m:msqrt></m:mrow>

<m:mrow><m:mn>2</m:mn></m:mrow>

</m:mfrac>

<m:mo>.</m:mo></m:mrow></m:math>

<div class="p"><!----></div>

Az öt érték között lehetnek egyenlőek. Le szeretnénk kódolni, hogy melyik értékből hány van. Az <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mo stretchy="false">(</m:mo><m:mn>1</m:mn><m:mo>,</m:mo><m:mn>1</m:mn><m:mo>,</m:mo><m:mn>3</m:mn><m:mo stretchy="false">)</m:mo></m:mrow></m:math> kódban a két egyes azt jelenti, hogy van két érték, amelyik csak egyszer-egyszer fordul elő, a hármas pedig azt, hogy van három kifejezés, amelynek ugyanaz az értéke. Mi a fenti öt számnak megfelelő kód?

<div class="p"><!----></div>

<br /><b>A)</b>&nbsp;&nbsp;&nbsp; <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mo stretchy="false">(</m:mo><m:mn>1</m:mn><m:mo>,</m:mo><m:mn>2</m:mn><m:mo>,</m:mo><m:mn>2</m:mn><m:mo stretchy="false">)</m:mo></m:mrow></m:math>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<b>B)</b>&nbsp;&nbsp;&nbsp; <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mo stretchy="false">(</m:mo><m:mn>1</m:mn><m:mo>,</m:mo><m:mn>1</m:mn><m:mo>,</m:mo><m:mn>3</m:mn><m:mo stretchy="false">)</m:mo></m:mrow></m:math>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <b>C)</b>&nbsp;&nbsp;&nbsp; <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mo stretchy="false">(</m:mo><m:mn>2</m:mn><m:mo>,</m:mo><m:mn>3</m:mn><m:mo stretchy="false">)</m:mo></m:mrow></m:math>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <b>D)</b>&nbsp;&nbsp;&nbsp; <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mo stretchy="false">(</m:mo><m:mn>1</m:mn><m:mo>,</m:mo><m:mn>4</m:mn><m:mo stretchy="false">)</m:mo></m:mrow></m:math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<b>E)</b>&nbsp;&nbsp;&nbsp; egyik sem<br />

y default: it reads from stdin and writes to stdout.

But a non-switch argument specifies the file[.tex] to translate to file.xml.

Diagnostics concerning unknown or untranslated constructs are sent to stderr.

<div class="p"><!----></div>

  Obtain USAGE </td><td width="150">

 switch information by:   ttm -?

  Obtain QUALIFICATIONS by:               ttm -?q

<div class="p"><!----></div>

TtM may be used and distributed under the terms of the GPL version 2.
<br />&nbsp;<br /><div align="right">[ <a class="link" href="exercise_box.php?mode=sne-s-j-&amp;label=A.I%3A%3Aa_i_gyok_060520_HAFT_04_teszt_01" target="_blank" onclick="mutat('exercise_box.php?mode=sne-s-j-&amp;label=A.I%3A%3Aa_i_gyok_060520_HAFT_04_teszt_01'); return false;">&nbsp;Megoldás&nbsp;</a>&nbsp;] </div></div>

<div class="feladat"><b>Feladat: 23.2.</b><br /> <a name="a_i_gyok_071128_teszt_ha_02" /><a href="bib_box.php?mode=sne---j-&amp;citation_num=" target="bib_box" onclick="mutat('bib_box.php?mode=sne---j-&amp;citation_num='); return false;"></a>Melyik a <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow>

<m:mfrac><m:mrow><m:msqrt><m:mrow><m:mn>7</m:mn></m:mrow></m:msqrt></m:mrow>

<m:mrow><m:msqrt><m:mrow><m:mn>8</m:mn></m:mrow></m:msqrt></m:mrow>

</m:mfrac>

</m:mrow></m:math> duplája?

<div class="p"><!----></div>

<br /><m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>U</m:mi><m:mo>=</m:mo>

<m:mfrac><m:mrow><m:msqrt><m:mrow><m:mn>14</m:mn></m:mrow></m:msqrt></m:mrow>

<m:mrow><m:msqrt><m:mrow><m:mn>8</m:mn></m:mrow></m:msqrt></m:mrow>

</m:mfrac>

</m:mrow></m:math>;

<br /><m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>&ensp;</m:mi></m:mrow></m:math><br />

<m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>V</m:mi><m:mo>=</m:mo>

<m:mfrac><m:mrow><m:msqrt><m:mrow><m:mn>28</m:mn></m:mrow></m:msqrt></m:mrow>

<m:mrow><m:msqrt><m:mrow><m:mn>8</m:mn></m:mrow></m:msqrt></m:mrow>

</m:mfrac>

</m:mrow></m:math>;

<br /><m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>&ensp;</m:mi></m:mrow></m:math><br />

<m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>X</m:mi><m:mo>=</m:mo>

<m:mfrac><m:mrow><m:msqrt><m:mrow><m:mn>7</m:mn></m:mrow></m:msqrt></m:mrow>

<m:mrow><m:msqrt><m:mrow><m:mn>4</m:mn></m:mrow></m:msqrt></m:mrow>

</m:mfrac>

</m:mrow></m:math>;

<br /><m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>&ensp;</m:mi></m:mrow></m:math><br />

<m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>Y</m:mi><m:mo>=</m:mo>

<m:mfrac><m:mrow><m:msqrt><m:mrow><m:mn>14</m:mn></m:mrow></m:msqrt></m:mrow>

<m:mrow><m:mn>2</m:mn></m:mrow>

</m:mfrac>

</m:mrow></m:math>.

<br />

<br /><b>A)</b>&nbsp;&nbsp;&nbsp; csak <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>U</m:mi></m:mrow></m:math>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<b>B)</b>&nbsp;&nbsp;&nbsp; csak <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>V</m:mi></m:mrow></m:math>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <b>C)</b>&nbsp;&nbsp;&nbsp; csak <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>X</m:mi></m:mrow></m:math>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <b>D)</b>&nbsp;&nbsp;&nbsp; csak <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>Y</m:mi></m:mrow></m:math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<b>E)</b>&nbsp;&nbsp;&nbsp; <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>V</m:mi></m:mrow></m:math> és <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>Y</m:mi></m:mrow></m:math><br />

y default: it reads from stdin and writes to stdout.

But a non-switch argument specifies the file[.tex] to translate to file.xml.

Diagnostics concerning unknown or untranslated constructs are sent to stderr.

<div class="p"><!----></div>

  Obtain USAGE </td><td width="150">

 switch information by:   ttm -?

  Obtain QUALIFICATIONS by:               ttm -?q

<div class="p"><!----></div>

TtM may be used and distributed under the terms of the GPL version 2.
<br />&nbsp;<br /><div align="right">[ <a class="link" href="exercise_box.php?mode=sne-s-j-&amp;label=A.I%3A%3Aa_i_gyok_071128_teszt_ha_02" target="_blank" onclick="mutat('exercise_box.php?mode=sne-s-j-&amp;label=A.I%3A%3Aa_i_gyok_071128_teszt_ha_02'); return false;">&nbsp;Megoldás&nbsp;</a>&nbsp;] </div></div>

<div class="feladat"><b>Feladat: 23.3.</b><br /> <a name="a_i_gyok_071128_teszt_ha_03" /><a href="bib_box.php?mode=sne---j-&amp;citation_num=" target="bib_box" onclick="mutat('bib_box.php?mode=sne---j-&amp;citation_num='); return false;"></a>Kocka felszíne 36 cm<m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow>

<m:msup><m:mrow></m:mrow><m:mrow><m:mn>2</m:mn></m:mrow>

</m:msup>

</m:mrow></m:math>. Mekkora a térfogata cm<m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow>

<m:msup><m:mrow></m:mrow><m:mrow><m:mn>3</m:mn></m:mrow>

</m:msup>

</m:mrow></m:math>-ben?

<br /><b>A)</b>&nbsp;&nbsp;&nbsp; 216&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<b>B)</b>&nbsp;&nbsp;&nbsp; 27&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <b>C)</b>&nbsp;&nbsp;&nbsp; <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mn>6</m:mn><m:msqrt><m:mrow><m:mn>6</m:mn></m:mrow></m:msqrt></m:mrow></m:math>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <b>D)</b>&nbsp;&nbsp;&nbsp; <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mn>3</m:mn><m:msqrt><m:mrow><m:mn>6</m:mn></m:mrow></m:msqrt></m:mrow></m:math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<b>E)</b>&nbsp;&nbsp;&nbsp; egyik sem<br />

y default: it reads from stdin and writes to stdout.

But a non-switch argument specifies the file[.tex] to translate to file.xml.

Diagnostics concerning unknown or untranslated constructs are sent to stderr.

<div class="p"><!----></div>

  Obtain USAGE </td><td width="150">

 switch information by:   ttm -?

  Obtain QUALIFICATIONS by:               ttm -?q

<div class="p"><!----></div>

TtM may be used and distributed under the terms of the GPL version 2.
<br />&nbsp;<br /><div align="right">[ <a class="link" href="exercise_box.php?mode=sne-s-j-&amp;label=A.I%3A%3Aa_i_gyok_071128_teszt_ha_03" target="_blank" onclick="mutat('exercise_box.php?mode=sne-s-j-&amp;label=A.I%3A%3Aa_i_gyok_071128_teszt_ha_03'); return false;">&nbsp;Megoldás&nbsp;</a>&nbsp;] </div></div>

<div class="feladat"><b>Feladat: 23.4.</b><br /> <a name="a_i_gyok_060520_HAFT_12_teszt_ha_04" /><a href="bib_box.php?mode=sne---j-&amp;citation_num=" target="bib_box" onclick="mutat('bib_box.php?mode=sne---j-&amp;citation_num='); return false;"></a>Az alábbi számkifejezések közül hánynak az értéke <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mn>40</m:mn></m:mrow></m:math>?

<br />

<m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>U</m:mi><m:mo>=</m:mo><m:msqrt><m:mrow><m:mn>1598</m:mn></m:mrow></m:msqrt><m:mo>+</m:mo><m:msqrt><m:mrow><m:mn>2</m:mn></m:mrow></m:msqrt></m:mrow></m:math><br /><m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>&ensp;</m:mi></m:mrow></m:math><br />

<br /><m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>&ensp;</m:mi></m:mrow></m:math><br />

<m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>V</m:mi><m:mo>=</m:mo><m:msqrt><m:mrow><m:mn>2</m:mn></m:mrow></m:msqrt><m:msqrt><m:mrow><m:mn>800</m:mn></m:mrow></m:msqrt></m:mrow></m:math><br /><m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>&ensp;</m:mi></m:mrow></m:math><br />

<br /><m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>&ensp;</m:mi></m:mrow></m:math><br />

<m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>X</m:mi><m:mo>=</m:mo><m:mn>5</m:mn><m:msqrt><m:mrow>

<m:msup><m:mrow><m:mn>2</m:mn></m:mrow><m:mrow><m:mn>6</m:mn></m:mrow>

</m:msup>

</m:mrow></m:msqrt></m:mrow></m:math><br /><m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>&ensp;</m:mi></m:mrow></m:math><br />

<br /><m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>&ensp;</m:mi></m:mrow></m:math><br />

<m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>Y</m:mi><m:mo>=</m:mo>

<m:mfrac><m:mrow><m:msqrt><m:mrow><m:mn>40</m:mn><m:mi>&ensp;</m:mi><m:mn>000</m:mn></m:mrow></m:msqrt></m:mrow>

<m:mrow><m:mn>5</m:mn></m:mrow>

</m:mfrac>

</m:mrow></m:math><br /><m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>&ensp;</m:mi></m:mrow></m:math><br />

<br /><m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>&ensp;</m:mi></m:mrow></m:math><br />

<m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>Z</m:mi><m:mo>=</m:mo><m:msqrt><m:mrow><m:mo stretchy="false">(</m:mo><m:mn>10</m:mn><m:mo>-</m:mo><m:mn>50</m:mn>

<m:msup><m:mrow><m:mo stretchy="false">)</m:mo></m:mrow><m:mrow><m:mn>2</m:mn></m:mrow>

</m:msup>

</m:mrow></m:msqrt></m:mrow></m:math>.

<br />

<div class="p"><!----></div>

<br /><b>A)</b>&nbsp;&nbsp;&nbsp; egynek&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<b>B)</b>&nbsp;&nbsp;&nbsp; kettőnek&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <b>C)</b>&nbsp;&nbsp;&nbsp; háromnak&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <b>D)</b>&nbsp;&nbsp;&nbsp; négynek &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<b>E)</b>&nbsp;&nbsp;&nbsp; ötnek vagy egynek sem<br />

y default: it reads from stdin and writes to stdout.

But a non-switch argument specifies the file[.tex] to translate to file.xml.

Diagnostics concerning unknown or untranslated constructs are sent to stderr.

<div class="p"><!----></div>

  Obtain USAGE </td><td width="150">

 switch information by:   ttm -?

  Obtain QUALIFICATIONS by:               ttm -?q

<div class="p"><!----></div>

TtM may be used and distributed under the terms of the GPL version 2.
<br />&nbsp;<br /><div align="right">[ <a class="link" href="exercise_box.php?mode=sne-s-j-&amp;label=A.I%3A%3Aa_i_gyok_060520_HAFT_12_teszt_ha_04" target="_blank" onclick="mutat('exercise_box.php?mode=sne-s-j-&amp;label=A.I%3A%3Aa_i_gyok_060520_HAFT_12_teszt_ha_04'); return false;">&nbsp;Megoldás&nbsp;</a>&nbsp;] </div></div>
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