Hi there!
――How come I must work overtime today!?
Around half a year later, since fresh out of college, I was too early to talk back to my senior at my trading company. Truth be told, I was immature and must have been a stuck-up brat for my senior employees.
We were in the middle of the high economic growth period when there were many free-lance, lordless samurai-type Shoushaman in the company. My irrational behavior was understandably unwelcome, and I might have been labeled as “a silo-mentality guy.”
I hadn’t been trained in anger management, and it goes without saying that I left the office with no ears to listen to my boss’s commands. Our Latin American Section must have had a lot on our plate.
An old cliché goes, “Wise men learn more from fools than fools from wise men.” I don’t think I’m a wise man; conversely, my bygone behavior of this didn’t allow me to learn something from seniors.
Too late, but my apologies to the then superiors. Forgive me for a series of irrational behaviors.
It is an onerous task to change irrational behavior into a rational one, so today, instead, let me identify the difference between rational and irrational numbers in mathematics.
\(\sqrt{3}\) is an irrational number. Find rational numbers \(a\) and \(b\) that satisfy the formula \(\frac{7 – a\sqrt{3}}{2 – \sqrt{3} }= b – 9\sqrt{3}\). (Rref. Yellow Chart Math Ⅰ＋Ａ P76, slightly changed the formula)
Here is my solution to the problem.
Convert the given formula as:
\(\frac{7 – a\sqrt{3}}{2 – \sqrt{3}} = \frac{(7 – a\sqrt{3})(2 + \sqrt{3})}{(2 – \sqrt{3})(2 + \sqrt{3})} = (14 – 3a) – (2a – 7)\sqrt{3}\)
Therefore, \((14 – 3a) – (2a – 7)\sqrt{3} = b – 9\sqrt{3}\).
\(14 – 3a, 2a – 7, b,\) and \(9\) are rational numbers, and \(\sqrt{3}\) an irratinal one. Then, \(14 – 3a = b\), and \(2a – 7 = 9\).
Finally, we get \(a = 8, b = -10\).
I’m clear about the difference between rational and irrational numbers, but not the subtle one between rational and irrational behaviors.
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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