$a=\sqrt{7}+\sqrt{5},\ b=\sqrt{7}-\sqrt{5}$とおく．
(1) $\displaystyle \frac{b}{a}=\fbox{ア}-\sqrt{\fbox{イウ}}$，$\displaystyle \frac{a}{b} = \fbox{エ}+\sqrt{\fbox{オカ}}$である．
(2) $\displaystyle \frac{b}{a},\ \frac{a}{b}$を解にもつ$2$次方程式は$x^2-\fbox{キク}x+\fbox{ケ}=0$と書くことができる．
(3) $A=\left( \begin{array}{cc} a & -b \\ \displaystyle\frac{1}{a} & \displaystyle\frac{1}{b} \end{array} \right)$とおくとき，$A$の逆行列$A^{-1}$は \[ A^{-1}=\left( \begin{array}{rr} \displaystyle\frac{\sqrt{7}}{\fbox{コサ}}+\frac{\sqrt{5}}{\fbox{シス}} & \displaystyle\frac{\sqrt{7}}{\fbox{セソ}}-\frac{\sqrt{5}}{\fbox{タチ}} \\ \\ -\displaystyle\frac{\sqrt{7}}{\fbox{ツテ}}+\frac{\sqrt{5}}{\fbox{トナ}} & \displaystyle\frac{\sqrt{7}}{\fbox{ニヌ}}+\frac{\sqrt{5}}{\fbox{ネノ}} \end{array} \right) \]