数研出版：これからの数学３

p.74 問1\(~~~\)(ア) \(a=1~,~b=3~,~c=2\)
\(~~~\)(ウ) \(a=8~,~b=0~,~c=-5\)
\(~~~\)(エ) \(a=1~,~b=3~,~c=0\)

p.75 問2\(\begin{split}~~~x=6~,~9\end{split}\)

p.75 問3\(\begin{split}~~~x=-1~,~3\end{split}\)

p.77 問1\(\begin{split}{\small (1)}~x=1~,~2\end{split}\)　　\(\begin{split}{\small (2)}~x=-5~,~6\end{split}\)
\(\begin{split}{\small (3)}~x=3~,~-5\end{split}\)　　\(\begin{split}{\small (4)}~x=-2~,~-4\end{split}\)
\(\begin{split}{\small (5)}~x=2~,~6\end{split}\)　　\(\begin{split}{\small (6)}~x=\pm3\end{split}\)

p.78 問2\(\begin{split}{\small (1)}~x=3~,~5\end{split}\)　　\(\begin{split}{\small (2)}~x=-1~,~-3\end{split}\)

p.79 問3\(\begin{split}{\small (1)}~x=0~,~-2\end{split}\)　　\(\begin{split}{\small (2)}~x=0~,~4\end{split}\)
\(\begin{split}{\small (3)}~x=0~,~-6\end{split}\)

p.79 問4\(\begin{split}{\small (1)}~x=-2\end{split}\)　　\(\begin{split}{\small (2)}~x=5\end{split}\)

p.80 問1\(\begin{split}{\small (1)}~x=\pm2\end{split}\)　　\(\begin{split}{\small (2)}~x=\pm\sqrt{5}\end{split}\)
\(\begin{split}{\small (3)}~x=\pm6\end{split}\)　　\(\begin{split}{\small (4)}~x=\pm3\sqrt{3}\end{split}\)

p.81 問2

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\(\begin{split}{\small (1)}~x=\pm\frac{\,1\,}{\,5\,}\end{split}\)　　\(\begin{split}{\small (2)}~x=\pm\frac{\,2\sqrt{2}\,}{\,3\,}\end{split}\)

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\(\begin{split}{\small (3)}~x=\pm\frac{\,3\,}{\,2\,}\end{split}\)　　\(\begin{split}{\small (4)}~x=\pm\frac{\,\sqrt{7}\,}{\,4\,}\end{split}\)

p.82 問3\(\begin{split}{\small (1)}~x=-5\pm\sqrt{6}\end{split}\)　　\(\begin{split}{\small (2)}~x=4~,~0\end{split}\)
\(\begin{split}{\small (3)}~x=-1~,~-7\end{split}\)　　\(\begin{split}{\small (4)}~x=1\pm2\sqrt{2}\end{split}\)

p.84 問4\(\begin{split}{\small (1)}~x=-4\pm\sqrt{11}\end{split}\)　　\(\begin{split}{\small (2)}~x=3\pm2\sqrt{2}\end{split}\)

p.84 問5\(\begin{eqnarray}~~~x^2+5x&=&2
\\[3pt]~~~x^2+5x+\frac{\,25\,}{\,4\,}&=&2+\frac{\,25\,}{\,4\,}
\\[3pt]~~~\left( x+\frac{\,5\,}{\,2\,} \right)^2&=&\frac{\,33\,}{\,4\,}
\\[3pt]~~~x+\frac{\,5\,}{\,2\,}&=&\pm\,\frac{\,\sqrt{33}\,}{\,2\,}
\\[3pt]~~~x&=&-\frac{\,5\,}{\,2\,}\pm\,\frac{\,\sqrt{33}\,}{\,2\,}
\end{eqnarray}\)

p.84 問6

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\(\begin{split}~~~x=-\frac{\,1\,}{\,2\,}\pm\frac{\,\sqrt{17}\,}{\,2\,}\end{split}\)

p.86 問1

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\(\begin{split}{\small (1)}~x=\frac{\,-7\pm\sqrt{41}\,}{\,4\,}\end{split}\)

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\(\begin{split}{\small (2)}~x=\frac{\,9\pm\sqrt{33}\,}{\,8\,}\end{split}\)

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\(\begin{split}{\small (3)}~x=\frac{\,-1\pm\sqrt{21}\,}{\,2\,}\end{split}\)

p.87 問2\(\begin{split}{\small (1)}~x=1\pm\sqrt{5}\end{split}\)　　\(\begin{split}{\small (2)}~x=\frac{\,4\pm3\sqrt{2}\,}{\,2\,}\end{split}\)

p.87 問3

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\(\begin{split}{\small (1)}~x=-2~,~\frac{\,3\,}{\,4\,}\end{split}\)　　\(\begin{split}{\small (2)}~x=3~,~-\frac{\,1\,}{\,2\,}\end{split}\)

p.88 問1\(\begin{split}{\small (1)}~x=-3~,~-7\end{split}\)　　\(\begin{split}{\small (2)}~x=0~,~5\end{split}\)

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\(\begin{split}{\small (3)}~x=-1~,~-4\end{split}\)　　\(\begin{split}{\small (4)}~x=\frac{\,7\pm\sqrt{41}\,}{\,2\,}\end{split}\)

p.88 問2　\(\begin{split}a=-5\end{split}\)
　もう１つの解は、\(\begin{split}x=2\end{split}\)

p.90 問1一番小さい方の自然数を \(x\) とすると、連続する３つの自然数は、
\(\begin{split}~~~x~,~x+1~,~x+2\end{split}\) となる
それぞれの２乗の和が \(110\) になることより、
\(\begin{eqnarray}~x^2+(x+1)^2+(x+2)^2&=&110
\\[2pt]~~~3x^2+6x-105&=&0
\\[2pt]~~~x^2+2x-35&=&0
\\[2pt]~~~(x+7)(x-5)&=&0
\\[2pt]~~~x&=&5~,~-7
\end{eqnarray}\)
\(x=-7\) のとき、自然数とならないので問題にあわない
\(x=5\) のとに、３つの自然数は \(5~,~6~,~7\) となり、問題にあう
よって、連続する３つの自然数は \(5~,~6~,~7\)

p.91 問2\(~~~1\) 秒後と \(5\) 秒後

p.93 問3\(\begin{split}~~~12~{\rm cm}\end{split}\)