1.次の計算をしなさい。
(1)\(x^2-3=0\)
\begin{eqnarray}x^2 &=& 3 \\ x &=& \pm\sqrt{3}\end{eqnarray}
(2)\(x^2-4=21\)
\begin{eqnarray}x^2 &=& 25 \\ x &=& \pm5\end{eqnarray}
(3)\(3y^2-6=0\)
\begin{eqnarray}y^2 &=& 2 \\ y &=& \pm\sqrt{2}\end{eqnarray}
(4)\(4x^2-5=0\)
\begin{eqnarray}x^2 &=& \frac{5}{4} \\ x &=& \pm\frac{\sqrt{5}}{2}\end{eqnarray}
(5)\(9x^2-6=4\)
\begin{eqnarray}x^2 &=& \frac{10}{9} \\ x &=& \pm\frac{\sqrt{10}}{3}\end{eqnarray}
(6)\(2x^2-3=5\)
\begin{eqnarray}x^2 &=& 4 \\ x &=& \pm2\end{eqnarray}
(7)\((x+4)^2=1\)
\[x+4=\pm1\] \begin{cases}x+4=1 \\ x+4=-1\end{cases} \[x=-3,x=-5\]
(8)\((x-3)^2=4\)
\[x-3=\pm2\] \begin{cases}x-3=2 \\ x-3=-2\end{cases} \[x=1,x=5\]
(9)\((x+2)^2-36=0\)
\[x+2=\pm6\] \begin{cases}x+2=6 \\ x+2=-6\end{cases} \[x=4,x=-8\]
(10)\((x-6)^2-40=9\)
\[x-6=\pm7\] \begin{cases}x-6=7 \\ x-6=-7\end{cases} \[x=13,x=-1\]
(11)\((x-5)^2=6\)
\begin{eqnarray}x-5 &=& \pm\sqrt{6} \\ x &=& 5\pm\sqrt{6}\end{eqnarray}
(12)\((x+1)^2-7=0\)
\begin{eqnarray}x+1 &=& \pm\sqrt{7} \\ x &=& -1\pm\sqrt{7}\end{eqnarray}
(13)\(3(x+2)^2=15\)
\begin{eqnarray}x+2 &=& \pm\sqrt{5} \\ x &=& -2\pm\sqrt{5}\end{eqnarray}
(14)\(4(x-4)^2+1=8\)
\begin{eqnarray}x-4 &=& \pm\frac{\sqrt{7}}{2} \\ x &=& 4\pm\frac{\sqrt{7}}{2}\end{eqnarray}
(15)\((x-8)(x-7)=0\)
\(x=7,x=8\)
(16)\(x(x-3)=0\)
\(x=0,x=3\)
(17)\(x^2+6x-7=0\)
\((x+1)(x-7)=0\)
\(x=-1,x=7\)
(18)\(x^2-5x+4=0\)
\((x-1)(x-4)=0\)
\(x=1,x=4\)
(19)\(x^2+8x=-15\)
\((x+3)(x+5)=0\)
\(x=-3,x=-5\)
(20)\(x^2-35=2x\)
\((x+5)(x-7)=0\)
\(x=-5,x=7\)
(21)\(x^2+2x=0\)
\(x(x+2)=0\)
\(x=0,x=-2\)
(22)\(x^2=7x\)
\(x(x-7)=0\)
\(x=0,x=7\)
(23)\((x+1)(x-2)=4\)
\(x^2-x-6=0\)
\((x+2)(x-3)=0\)
\(x=-2,x=3\)
(24)\((x-3)(x-5)=3\)
\(x^2-8x+12=0\)
\((x-2)(x-6)=0\)
\(x=2,x=6\)
(25)\((x-5)(x+1)=-5\)
\(x^2-4x=0\)
\(x(x-4)=0\)
\(x=0,x=4\)
(26)\((x+2)(x+4)=-3x\)
\(x^2+9x+8=0\)
\((x+1)(x+8)=0\)
\(x=-1,x=-8\)
(27)\(x^2+12x+11=0\)
\((x+1)(x+11)=0\)
\(x=-1,x=-11\)
(28)\(x^2-8x+16=0\)
\((x-4)^2=0\)
\(x=4\)
(29)\(x^2-2x-48=0\)
\((x+6)(x-8)=0\)
\(x=-6,x=8\)
(30)\((x-3)(x+1)=12\)
\(x^2-2x-15=0\)
\((x+3)(x-5)=0\)
\(x=-3,x=5\)
(31)\(x^2+5x+2=0\)
\(x=\frac{-5\pm\sqrt{5^2-4×1×2}}{2×1}\)
\(\ \ =\frac{-5\pm\sqrt{17}}{2}\)
(32)\(x^2+7x-3=0\)
\(x=\frac{-7\pm\sqrt{7^2-4×1×(-3)}}{2×1}\)
\(\ \ =\frac{-7\pm\sqrt{61}}{2}\)
(33)\(x^2-3x-6=0\)
\(x=\frac{-(-3)\pm\sqrt{(-3)^2-4×1×(-6)}}{2×1}\)
\(\ \ =\frac{3\pm\sqrt{33}}{2}\)
(34)\(2x^2+5x+1=0\)
\(x=\frac{-5\pm\sqrt{5^2-4×2×1}}{2×2}\)
\(\ \ =\frac{-5\pm\sqrt{17}}{4}\)
(35)\(3x^2-9x+5=0\)
\(x=\frac{-(-9)\pm\sqrt{(-9)^2-4×3×5}}{2×3}\)
\(\ \ =\frac{9\pm\sqrt{21}}{6}\)
(36)\(6x^2-x-4=0\)
\(x=\frac{-(-1)\pm\sqrt{(-1)^2-4×6×(-4)}}{2×6}\)
\(\ \ =\frac{1\pm\sqrt{97}}{12}\)
(37)\(x^2+4x+2=0\)
\(x=\frac{-4\pm\sqrt{4^2-4×1×2}}{2×1}\)
\(\ \ =\frac{-4\pm\sqrt{8}}{2}\)
\(\ \ =\frac{-4\pm2\sqrt{2}}{2}\)
\(\ \ =-2\pm\sqrt{2}\)
(38)\(2x^2+8x-7=0\)
\(x=\frac{-8\pm\sqrt{8^2-4×2×(-7)}}{2×2}\)
\(\ \ =\frac{-8\pm\sqrt{120}}{4}\)
\(\ \ =\frac{-8\pm2\sqrt{30}}{4}\)
\(\ \ =\frac{-4\pm\sqrt{30}}{2}\)
(39)\(5x^2-6x=4\)
\(x=\frac{-(-6)\pm\sqrt{(-6)^2-4×5×(-4)}}{2×5}\)
\(\ \ =\frac{6\pm\sqrt{116}}{10}\)
\(\ \ =\frac{6\pm2\sqrt{29}}{10}\)
\(\ \ =\frac{3\pm\sqrt{29}}{5}\)
(40)\(3x^2=10x-2\)
\(x=\frac{-(-10)\pm\sqrt{(-10)^2-4×3×2}}{2×3}\)
\(\ \ =\frac{10\pm\sqrt{76}}{6}\)
\(\ \ =\frac{10\pm2\sqrt{19}}{6}\)
\(\ \ =\frac{5\pm\sqrt{19}}{3}\)
(41)\(x(2x+5)=3\)
\(x=\frac{-5\pm\sqrt{5^2-4×2×(-3)}}{2×2}\)
\(\ \ =\frac{-5\pm\sqrt{49}}{4}\)
\(\ \ =\frac{-5\pm7}{4}\)
\(x=\frac{1}{2},x=-3\)
(42)\(2x(x-3)+3=0\)
\(x=\frac{-(-6)\pm\sqrt{(-6)^2-4×2×3}}{2×2}\)
\(\ \ =\frac{6\pm\sqrt{12}}{4}\)
\(\ \ =\frac{6\pm2\sqrt{3}}{4}\)
\(\ \ =\frac{3\pm\sqrt{3}}{2}\)
(43)\(x^2-75=0\)
\begin{eqnarray}x^2 &=& 75 \\ x &=& \pm\sqrt{75} \\ x &=& \pm5\sqrt{3}\end{eqnarray}
(44)\((x-3)^2=16\)
\[x-3=\pm4\] \begin{cases}x-3=4 \\ x-3=-4\end{cases} \[x=7,x=-1\]
(45)\((x+10)^2-3=0\)
\[x+10=\pm\sqrt{3}\] \[x=-10\pm\sqrt{3}\]
(46)\(2(x+5)^2=18\)
\[x+5=\pm3\] \begin{cases}x+5=3 \\ x+5=-3\end{cases} \[x=-2,x=-8\]
(47)\(x^2-8x+12=0\)
\[(x-2)(x-6)=0\] \[x=2,x=6\]
(48)\(x^2-6x-16=0\)
\[(x+2)(x-8)=0\] \[x=-2,x=8\]
(49)\(x^2+16x+64=0\)
\[(x+8)^2=0\] \[x=-8\]
(50)\(x^2-5x=0\)
\[x(x-5)=0\] \[x=0,x=5\]
(51)\(x^2-7x+1=0\)
\(x=\frac{-(-7)\pm\sqrt{(-7)^2-4×1×1}}{2×1}\)
\(\ \ =\frac{7\pm\sqrt{45}}{2}\)
\(\ \ =\frac{7\pm3\sqrt{5}}{2}\)
(52)\(x^2+6x-2=0\)
\(x=\frac{-6\pm\sqrt{6^2-4×1×(-2)}}{2×1}\)
\(\ \ =\frac{-6\pm\sqrt{44}}{2}\)
\(\ \ =\frac{-6\pm2\sqrt{11}}{2}\)
\(\ \ =-3\pm\sqrt{11}\)
(53)\(4x^2-5x-2=0\)
\(x=\frac{-(-5)\pm\sqrt{(-5)^2-4×4×(-2)}}{2×4}\)
\(\ \ =\frac{5\pm\sqrt{57}}{8}\)
(54)\(2x^2+4x-1=0\)
\(x=\frac{-4\pm\sqrt{4^2-4×2×(-1)}}{2×2}\)
\(\ \ =\frac{-4\pm\sqrt{24}}{4}\)
\(\ \ =\frac{-4\pm2\sqrt{6}}{4}\)
\(\ \ =\frac{-2\pm\sqrt{6}}{2}\)
(55)\(0.1x^2+0.5x-1.4=0\)
\(x^2+5x-14=0\)
\((x-2)(x+7)=0\)
\(x=2,x=-7\)
(56)\(\frac{3}{4}x^2-\frac{1}{2}x=\frac{5}{6}\)
\(9x^2-6x-10=0\)
\(x=\frac{-(-6)\pm\sqrt{(-6)^2-4×9×(-10)}}{2×9}\)
\(\ \ =\frac{6\pm\sqrt{396}}{18}\)
\(\ \ =\frac{6\pm6\sqrt{11}}{18}\)
\(\ \ =\frac{1\pm\sqrt{11}}{3}\)
(57)\(7x^2-2=5\)
\begin{eqnarray}7x^2 &=& 7 \\ x^2 &=& 1 \\ x &=& \pm1\end{eqnarray}
(58)\(6(x-1)^2=18\)
\[(x-1)^2=3\] \[x-1=\pm\sqrt{3}\] \[x=1\pm\sqrt{3}\]
(59)\(x^2+8x+15=0\)
\[(x+3)(x+5)=0\] \[x=-3,x=-5\]
(60)\(y^2=3y+15\)
\(y^2-3y-15=0\)
\(y=\frac{-(-3)\pm\sqrt{(-3)^2-4×1×(-15)}}{2×1}\)
\(\ \ =\frac{3\pm\sqrt{69}}{2}\)
(61)\(x^2-12=4x\)
\[x^2-4x-12=0\] \[(x-6)(x+2)=0\] \[x=6,x=-2\]
(62)\(5x^2-1=2x\)
\(5x^2-2x-1=0\)
\(x=\frac{-(-2)\pm\sqrt{(-2)^2-4×5×(-1)}}{2×5}\)
\(\ \ =\frac{2\pm\sqrt{24}}{10}\)
\(\ \ =\frac{2\pm2\sqrt{6}}{10}\)
\(\ \ =\frac{1\pm\sqrt{6}}{5}\)
(63)\((x-5)(x-6)=6\)
\[x^2-11x+24=0\] \[(x-3)(x-8)=0\] \[x=3,x=8\]
(64)\((x-3)^2=x-2\)
\(x^2-7x+11=0\)
\(x=\frac{-(-7)\pm\sqrt{(-7)^2-4×1×11}}{2×1}\)
\(\ \ =\frac{7\pm\sqrt{5}}{2}\)
(65)\((x+2)(x-4)=3x\)
\(x^2-5x-8=0\)
\(x=\frac{-(-5)\pm\sqrt{(-5)^2-4×1×(-8)}}{2×1}\)
\(\ \ =\frac{5\pm\sqrt{57}}{2}\)
(66)\(x(x-5)=2\)
\(x^2-5x-2=0\)
\(x=\frac{-(-5)\pm\sqrt{(-5)^2-4×1×(-2)}}{2×1}\)
\(\ \ =\frac{5\pm\sqrt{33}}{2}\)
(67)\(3x^2+12x-18=0\)
\(x^2+4x-6=0\)
\(x=\frac{-4\pm\sqrt{4^2-4×1×(-6)}}{2×1}\)
\(\ \ =\frac{-4\pm\sqrt{40}}{2}\)
\(\ \ =\frac{-4\pm2\sqrt{10}}{2}\)
\(\ \ =-2\pm\sqrt{10}\)
(68)\(-x^2-3x-2=0\)
\[x^2+3x+2=0\] \[(x+1)(x+2)=0\] \[x=-1,x=-2\]