高校受験数学/解答と解説のソースを表示

== 大問1 ==
=== 解答 ===
#<math>4\sqrt{2}</math>
#<math>x^{16}+x^8+1</math>
#<math>\left(x^2+1\right)\left(x+1\right)\left(x-1\right)</math>
#''a'' ≦ -7
#''a'' < 10
#''b'' = 4
#小問の解答
##<math>a = \sqrt{2}</math>
##<math>x = 2 \pm \sqrt{3}</math>
##''t'' = 2.75, 3

=== 解説 ===
==== 問1 ====
<div class="editsection" style="color:#000;background:#ffffff;font-size:larger;text-align:left;margin:0.5em 5px 0;padding:0.6em 0;border:2px solid #6f8f9f"><math>\displaystyle
\frac{\left(\sqrt{18}-2\sqrt{50}+
\displaystyle \frac{6}{\sqrt{2}}\right)^2}
{5\sqrt{2}+\sqrt{162}-\sqrt{200}}</math>を計算せよ。</div>
<math>
\begin{matrix}
&=& \displaystyle\frac{\left(3\sqrt{2}-10\sqrt{2}+3\sqrt{2}\right)^2}
{5\sqrt{2}+9\sqrt{2}-10\sqrt{2}} \\
&=& \displaystyle \frac{\left(-4\sqrt{2}\right)^2}{4\sqrt{2}} \\
&=& \displaystyle \frac{\left(4\sqrt{2}\right)^2}{4\sqrt{2}} \\
&=& \underline{\underline{4\sqrt{2}}}
\end{matrix}
</math>

==== 問2 ====
<div class="editsection" style="color:#000;background:#ffffff;font-size:larger;text-align:left;margin:0.5em 5px 0;padding:0.6em 0;border:2px solid #6f8f9f"><math>
(x^2+x+1)(x^2-x+1)(x^4- ''x''^2 + 1)(x^8 - x^4 + 1)</math>を展開せよ。
</div>
<math>
\begin{matrix}
&=& \left\{\left(x^2+x+1\right)
\left(x^2-x+1\right)\right\}
\left(x^4-x^2+1\right)\left(x^8-x^4+1\right) \\
&=& \left\{\left(x^4+2x^2+1\right)-x^2\right\}
\left(x^4-x^2+1\right)\left(x^8-x^4+1\right) \\
&=& \left(x^4+x^2+1\right)\left(x^4-x^2+1\right)\left(x^8-x^4+1\right) \\
&=& \left(x^8+x^4+1\right)\left(x^8-x^4+1\right) \\
&=& \underline{\underline{x^{16} + x^8 + 1}}
\end{matrix}
</math>

左から掛けていくと、次々に和と差の積の公式が使える形が表れていくのがポイントである。

==== 問4 ====

==== 問5 ====


== 大問2 ==
=== (1) ===
=== (2) ===

[[カテゴリ:数学]]