x=a+1ax2=(a+1a)2=a2+2+1a2x = a + \frac{1}{a} \qquad x^2 = \left(a+\frac{1}{a}\right)^2 = a^2+2+\frac{1}{a^2}x=a+a1x2=(a+a1)2=a2+2+a21 x+x2−4=a+1a+a2+2+1a2−4=a+1a+a2−2+1a2=a+1a+(a−1a)2=(a+1a)+∣a−1a∣x+\sqrt{x^2-4} = a+\frac{1}{a}+\sqrt{a^2+2+\frac{1}{a^2}-4} = a+\frac{1}{a}+\sqrt{a^2-2+\frac{1}{a^2}} = a+\frac{1}{a}+\sqrt{\left(a-\frac{1}{a}\right)^2} = \left(a+\frac{1}{a}\right)+\left|a-\frac{1}{a}\right|x+x2−4=a+a1+a2+2+a21−4=a+a1+a2−2+a21=a+a1+(a−a1)2=(a+a1)+a−a1 a≥1a \geq 1a≥1 より a+1a+a−1a=2aa+\frac{1}{a}+a-\frac{1}{a} = 2aa+a1+a−a1=2a