日本文教出版：中学数学３

p.70 問1　\(a=1~,~b=-10~,~c=24\)

p.70 問2　(ア) \(a=3~,~b=-4~,~c=-2\)
　(ウ) \(a=1~,~b=0~,~c=-5\)

p.71 問3　\(x=4~,~6\)

p.71 問4\(\begin{split}{\small (1)}~\end{split}\)解でない　　\(\begin{split}{\small (2)}~\end{split}\)解である
\(\begin{split}{\small (3)}~\end{split}\)解である

p.71 問5\(\begin{split}{\small (1)}~\end{split}\)解である　　\(\begin{split}{\small (2)}~\end{split}\)解でない
\(\begin{split}{\small (3)}~\end{split}\)解である　　\(\begin{split}{\small (4)}~\end{split}\)解である

p.72 問1\(\begin{split}{\small (1)}~x=2~,~-5\end{split}\)　　\(\begin{split}{\small (2)}~x=-3~,~-4\end{split}\)
\(\begin{split}{\small (3)}~x=0~,~3\end{split}\)　　\(\begin{split}{\small (4)}~y=0~,~-1\end{split}\)

p.73 問2\(\begin{split}{\small (1)}~x=0~,~-7\end{split}\)　　\(\begin{split}{\small (2)}~a=0~,~2\end{split}\)
\(\begin{split}{\small (3)}~x=-1~,~-4\end{split}\)　　\(\begin{split}{\small (4)}~y=1~,~2\end{split}\)
\(\begin{split}{\small (5)}~x=\pm\,5\end{split}\)　　\(\begin{split}{\small (6)}~x=3~,~-4\end{split}\)

p.73 問3\(\begin{split}{\small (1)}~x=-5\end{split}\)　　\(\begin{split}{\small (2)}~x=6\end{split}\)

p.73 問4　\(x=0\) のとき、両辺を \(x\) で割れない
　正しい解は \(x=0~,~9\)

p.74 問1　(ア) \(-5\) を移項
　(イ) 両辺を \({\, \small \div \,} 4\)

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　(ウ) \(x\) は \(\begin{split}\frac{\,5\,}{\,4\,}\end{split}\) の平方根

p.74 問2\(\begin{split}{\small (1)}~x=\pm\,\sqrt{5}\end{split}\)　　\(\begin{split}{\small (2)}~a=\pm\,2\sqrt{3}\end{split}\)
\(\begin{split}{\small (3)}~x=\pm\,5\sqrt{2}\end{split}\)　　\(\begin{split}{\small (4)}~x=\pm\,\sqrt{3}\end{split}\)

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\(\begin{split}{\small (5)}~a=\pm\,2\sqrt{7}\end{split}\)　　\(\begin{split}{\small (6)}~x=\pm\,\frac{\,4\,}{\,3\,}\end{split}\)

p.75 問3\(\begin{split}{\small (1)}~x=5\pm\,\sqrt{3}\end{split}\)　　\(\begin{split}{\small (2)}~x=-3\pm\,\sqrt{7}\end{split}\)
\(\begin{split}{\small (3)}~x=-2\pm\,2\sqrt{2}\end{split}\)　　\(\begin{split}{\small (4)}~x=4~,~8\end{split}\)

p.75 問4　\(x=-3\pm\,\sqrt{2}\)

p.75 問5\(\begin{eqnarray}~~~x^2+4x+1&=&0
\\[2pt]~~~x^2+4x&=&-1
\\[2pt]~~~x^2+4x+4&=&-1+4
\\[2pt]~~~(x+2)^2&=&3
\\[2pt]~~~x+2&=&\pm\,\sqrt{3}
\\[2pt]~~~x&=&-2\pm\,\sqrt{3}
\end{eqnarray}\)

p.75 問6　\(x=-4\pm\,\sqrt{2}\)

p.77 問1

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\(\begin{split}{\small (1)}~x=\frac{\,-7\pm\,\sqrt{37}\,}{\,6\,}\end{split}\)

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

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\(\begin{split}{\small (3)}~x=\frac{\,-5\pm\,\sqrt{57}\,}{\,2\,}\end{split}\)

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\(\begin{split}{\small (4)}~x=\frac{\,1\pm\,\sqrt{61}\,}{\,10\,}\end{split}\)

p.77 問2

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\(\begin{split}{\small (1)}~x=-1\pm\,\sqrt{6}\end{split}\)　　\(\begin{split}{\small (2)}~x=\frac{\,4\pm\,\sqrt{2}\,}{\,2\,}\end{split}\)

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\(\begin{split}{\small (3)}~x=\frac{\,3\pm\,\sqrt{15}\,}{\,2\,}\end{split}\)　　\(\begin{split}{\small (4)}~x=-4\pm\,2\sqrt{5}\end{split}\)

p.78 問3

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

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\(\begin{split}{\small (3)}~x=-3~,~\frac{\,1\,}{\,2\,}\end{split}\)　　\(\begin{split}{\small (4)}~x=1~,~-\frac{\,4\,}{\,5\,}\end{split}\)

p.78 問4\(\begin{split}{\small (1)}~x=2~,~7\end{split}\)　　\(\begin{split}{\small (2)}~x=\pm\,\sqrt{17}\end{split}\)

p.78 問5\(\begin{split}{\small (1)}~x=-3~,~-9\end{split}\)　　\(\begin{split}{\small (2)}~x=3\pm\,\sqrt{6}\end{split}\)
\(\begin{split}{\small (3)}~x=\pm\,\sqrt{6}\end{split}\)　　\(\begin{split}{\small (4)}~x=8~,~10\end{split}\)

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\(\begin{split}{\small (5)}~x=-\frac{\,1\,}{\,3\,}\end{split}\)　　\(\begin{split}{\small (6)}~x=1~,~-3\end{split}\)

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\(\begin{split}{\small (7)}~x=\frac{\,1\pm\,\sqrt{5}\,}{\,2\,}\end{split}\)　　\(\begin{split}{\small (8)}~x=-\frac{\,1\,}{\,2\,}~,~\frac{\,1\,}{\,3\,}\end{split}\)

p.79 問1\(\begin{split}{\small (1)}~x=3~,~4\end{split}\)
\(\begin{split}{\small (2)}~x=5\end{split}\)

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\(\begin{split}{\small (3)}~x=\frac{\,-5\pm\,\sqrt{57}\,}{\,2\,}\end{split}\)

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\(\begin{split}{\small (4)}~x=-2~,~-10\end{split}\)

p.79 問2　\(a=2\)
　もう１つの解は \(x=-5\)

p.80 基本の問題 1\(\begin{split}{\small (1)}~\end{split}\)解でない　　\(\begin{split}{\small (2)}~\end{split}\)解である

p.80 基本の問題 2\(\begin{split}{\small (1)}~x=-1~,~-9\end{split}\)　　\(\begin{split}{\small (2)}~y=0~,~-5\end{split}\)
\(\begin{split}{\small (3)}~x=-2~,~-7\end{split}\)　　\(\begin{split}{\small (4)}~x=5~,~-6\end{split}\)
\(\begin{split}{\small (5)}~a=1~,~6\end{split}\)　　\(\begin{split}{\small (6)}~a=\pm\,9\end{split}\)
\(\begin{split}{\small (7)}~x=-3~,~11\end{split}\)　　\(\begin{split}{\small (8)}~x=7\end{split}\)

p.80 基本の問題 3\(\begin{split}{\small (1)}~x=\pm\,\sqrt{3}\end{split}\)　　\(\begin{split}{\small (2)}~a=\pm\,2\sqrt{2}\end{split}\)

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

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\(\begin{split}{\small (5)}~x=1\pm\,\sqrt{5}\end{split}\)　　\(\begin{split}{\small (6)}~x=-6\pm\,2\sqrt{3}\end{split}\)

p.80 基本の問題 4

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\(\begin{split}{\small (1)}~x=\frac{\,-5\pm\,\sqrt{17}\,}{\,4\,}\end{split}\)　　\(\begin{split}{\small (2)}~x=\frac{\,7\pm\,\sqrt{5}\,}{\,2\,}\end{split}\)

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\(\begin{split}{\small (3)}~x=\frac{\,3\pm\,3\sqrt{5}\,}{\,2\,}\end{split}\)　　\(\begin{split}{\small (4)}~x=-3\pm\,\sqrt{6}\end{split}\)

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\(\begin{split}{\small (5)}~x=1\pm\,\sqrt{2}\end{split}\)　　\(\begin{split}{\small (6)}~x=\frac{\,-2\pm\,3\sqrt{2}\,}{\,2\,}\end{split}\)

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\(\begin{split}{\small (7)}~x=1~,~\frac{\,1\,}{\,3\,}\end{split}\)　　\(\begin{split}{\small (8)}~x=-2~,~\frac{\,1\,}{\,4\,}\end{split}\)

p.80 基本の問題 5\(\begin{split}{\small (1)}~x=-1~,~-7\end{split}\)　　\(\begin{split}{\small (2)}~x=4\pm\,2\sqrt{2}\end{split}\)
\(\begin{split}{\small (3)}~x=1~,~-5\end{split}\)　　\(\begin{split}{\small (4)}~x=-1~,~6\end{split}\)

p.81 問1\(\begin{split}{\small (1)}~7\end{split}\)　　\(\begin{split}{\small (2)}~2~,~-8\end{split}\)

p.82 問2　縦の長さ \(10~{\rm m}\)、横の長さ \(20~{\rm m}\)

p.82 問3　\(4~{\rm cm}~,~7~{\rm cm}\)

p.83 問4　\(4~{\rm cm}~,~16~{\rm cm}\)

p.83 問5　\(1~{\rm cm}\)