問題
問1．\(x=\sqrt{2}+\sqrt{3}\)とする．このとき，次の式を計算せよ．
(1) \(\displaystyle x+\frac{1}{x}\)
(2) \(\displaystyle x^2+\frac{1}{x^2}\)
(3) \(\displaystyle x^3+\frac{1}{x^3}\)
(4) \(\displaystyle x^4+\frac{1}{x^4}\)
問2．\(\displaystyle x=\frac{1}{\sqrt{5}+1}，\displaystyle y=\frac{1}{\sqrt{5}-1}\)とする．このとき，次の式を計算せよ．
(1) \(x+y\)
(2) \(x-y\)
(3) \(xy\)
(4) \(x^2+y^2\)
(5) \(x^2-y^2\)
(6) \(x^3+y^3\)
(7) \(x^3-y^3\)
(8) \(x^4-y^4\)
解答
