第2章 2.16

(1)

11+2+3=1+23(1+2)23=1+231+22+23=1+2322=2+264=2+264\frac{1}{1+\sqrt{2}+\sqrt{3}} = \frac{1+\sqrt{2}-\sqrt{3}}{\left(1+\sqrt{2}\right)^2-3} = \frac{1+\sqrt{2}-\sqrt{3}}{1+2\sqrt{2}+2-3} = \frac{1+\sqrt{2}-\sqrt{3}}{2\sqrt{2}} = \frac{\sqrt{2}+2-\sqrt{6}}{4} = \frac{2+\sqrt{2}-\sqrt{6}}{4}

(2)

12+3+5=2+35(2+3)25=2+352+26+35=2+3526=23+323012\frac{1}{\sqrt{2}+\sqrt{3}+\sqrt{5}} = \frac{\sqrt{2}+\sqrt{3}-\sqrt{5}}{\left(\sqrt{2}+\sqrt{3}\right)^2-5} = \frac{\sqrt{2}+\sqrt{3}-\sqrt{5}}{2+2\sqrt{6}+3-5} = \frac{\sqrt{2}+\sqrt{3}-\sqrt{5}}{2\sqrt{6}} = \frac{2\sqrt{3}+3\sqrt{2}-\sqrt{30}}{12}

解説: r31bn1z