Hi there!
We had several sections in the Export Department at my trading company. As I mentioned earlier, I had bad chemistry with the Department Director and ended up working directly under the Senior Executive officer.
I was not relegated to a declining and financially precarious export section; the company allowed me to work in a more robust decision-making section that supervised all the export operations. Sounds contradictory, doesn’t it?
Sooner after I had started working under the Senior Executive Director, I found some sections unnecessarily unproductive due to their overtime work.
I lost no time in scrutinizing the root cause of their unproductivity. Truth be told, their old-fashioned bureaucratic procedures and face time made the staff gauge their boss’s feelings, eventually bringing them to unnecessary overtime work.
Don’t take me wrong; I was not a person who swaggered about under borrowed authority of my senior. That being said, I could successfully take a comprehensive, panoramic view of all the operations concerned, thanks to my newly assigned position.
Today, let me challenge a word problem related to root, by which, presumably, I may be able to identify the root cause of why I have yet to reach a master of mathematics. Sounds incomprehensible?
Evaluate \(\frac{\sqrt{x^{4} – 10x^{3} + 25x^{2} – 10x + 1}}{x}\) providing \(x + \frac{1}{x} = 5 – \sqrt{5}\). (Ref: Enjoy Math to Become Mathy)
Here is my solution to the problem.
Firstly, given the condition \(x + \frac{1}{x} = 5 – \sqrt{5}\), we get \(x > 0\).
Then insert \(x\) into the numerator of the formula as
\(\sqrt{\frac{x^{4} – 10x^{3} + 25x^{2} – 10x + 1}{x^{2}}}\)
Organize the inside of the root for the given condition to be plugged in easily.
\(\sqrt{(x + \frac{1}{x})^{2} – 10(x + \frac{1}{x}) + 23}\)
\(= \sqrt{(5 – \sqrt{5})^{2} – 10(5 – \sqrt{5}) + 23}\)
\(= \sqrt{3}\)
Special thanks to: Enjoy Math to Become Mathy
This Youtube Site helps me with a brain teaser.
The root cause of my destructive creativity might be an inherent sense of humanities.
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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