Hi there!
The scenery that put me in awe on my business trip to South Africa was Table Mountain out there. On a crisp autumn Sunday morning, one of my clients took me to one of my best memorable landscapes.
On top of the mountain, we sat on the ground silently without communicating; if I remember correctly, we just watched the natural arts like painting for almost 30 minutes――tableau, that’s the word.
I’m not interested in any sightseeing spots, but not a soul was to be seen that day, and I could freshen myself out of my fatigue as an expatriate staying abroad long.
――Not failure, but low aim is a crime.
I decided to give it a shot to weather whatever storm I encountered and to become a Shoushaman of a high caliber. I was geared up to stick to my goals and make them happen.
I found the Japanese word “Kowai” (scary) in the exercise book Chart Ⅰ＋A in Chapter 1: Real Number. Such a frightening problem in mathematics gives me an awesome or incredible feeling. Nothing can stop my curiosity until I’m perfectly convinced in theory.
Denest the radicals \(-\sqrt{(-a)^{2}} + \sqrt{a^{2}(a – 1)^{2}}\) for its simplification, in the conditions of: (1) \(a\geq 1\), (2) \(0\leq a<1\), and (3) \(a<0\). (Source: Chart Mathematics Ⅰ＋Ａ Double Radical Sign)
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新品価格 |
The exercise book says, “Remember \(\sqrt{(Kowai (scary))^{2}}\) on right, bottom of page 40. Let me bear that in mind and solve the word problem.
Put an absolute value symbol after denesting the radicals by condition.
\(-\sqrt{(-a)^{2}} + \sqrt{a^{2}(a – 1)^{2}}\)
\(= -|a|+|a||a – 1|\)
\(= |a|(|a – 1| – 1)\)・・・・・（＊）
Now let’s find the answer to the formula by division.
(1) At \(a\geq 1\)
\(|a| = a, |a – 1| = a – 1\)
Therefore,（＊）becomes \(a^{2} – 2a\).
(2) At \(0\leq a<1\)
\(|a| = a, |a – 1| = -(a – 1)\)
Therefore,（＊）becomes \(-a^{2}\).
(3) At \(a<0\)
\(|a| = -a, |a – 1| = -(a – 1)\)
Therefore,（＊）becomes \(a^{2}\).
So scary or awesome about the absolute value am I that I’ve solved the problem discreetly.
Last but not least, you may listen to My Memory in Cape Town. Thanks.
Stay tuned, and expect to see my next post.
Keep well.
Frank Yoshida
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【グローバルビジネスで役立つ数学】でもっと学習する b＾＾)
【参考図書】『もう一度高校数学』（著者：高橋一雄氏）株式会社日本実業出版社
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