グローバルビジネスで役立つ数学(52)コーシー・シュワルツの不等式(英語版)

Hi there!

How many times have you thought you are maltreated in the workplace? Too much sales quota imposed by your boss? Unfairly relegated to a branch office? Or you’ve been sued for power harassment, an instructive or didactic attitude misconstrued as overbearingness?

I also experienced unfairness or inequality while working at a trading company. “Because I am so good-natured, I am probably forced to take on an excessively demanding task,” so much so that I got paranoid, and I was in for a sleepless night with so much chagrin.

It was one such day; however, a maxim helped me have positive thinking to accept the truth in our lives. That is,

――Life is unfair.

I realized we must grab or capture equality and fairness ourselves; it is not a given thing. Be positive and proactive; as a cliché goes, “Every cloud has a silver lining.”

Today, let me prove an inequality by using Cauchy–Schwarz inequality.

Prove the inequality \(x^{2} + y^{2} + z^{2}\geq 3\), given \(x\), \(y\), and \(z\) are all real numbers and \(x + y + z = 3\).

Here is my solution to the problem.

From Cauchy-Schwarz inequality,

\((1^{2} + 1^{2} + 1^{2})(x^{2} + y^{2} + z^{2})\geq(1・x + 1・y + 1・z)^{2}\)
\(3(x^{2} + y^{2} + z^{2})\geq 3^{2}\)
Therefore, \(x^{2} + y^{2} + z^{2}\geq 3\)

The above formula has equality at \(\frac{x}{1} = \frac{y}{1} = \frac{z}{1}\), and \(x = y = z = 1\) from \(x + y + z = 3\).

Thus, \(x^{2} + y^{2} + z^{2}\geq 3\).

Life and mathematics are both unfair, aren’t they?

Stay tuned, and expect to see my next post.

Keep well.

Frank Yoshida

 ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄
【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
【レッスン】私のオンライン英語レッスンをご希望の方はこちらをご覧ください。
【コンテント】当サイトで提供する情報はその正確性と最新性の確保に努めていま
 すが完全さを保証するものではありません。当サイトの内容に関するいかなる間
 違いについても一切の責任を負うものではありません

 

 ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄
只今、人気ブログランキングに参加しています。
今日の[実践数学の達人]のランキングは――


数学ランキング