グローバルビジネスで役立つ数学（25）灘高校の入試問題に挑戦（英語版）

Hi, there!

One of Japan’s most prestigious high schools is Nada Senior High School.
I don’t have any old friends from that high school, but I have run into a few
students who might have been enrolled in it.

Accidentally, I got on the same train as they did, and it was mind-boggling
for me to hear their conversations. They were talking about one of the mas-
terpieces written by a famous Japanese novelist and enjoying a conversa-
tion about his taste for the stories.

I often overhear passengers’ loud whispers; however, it was an absolutely
different world you never see in commoners’ talks. I got the impression
that their epistemic curiosity was overwhelming our secular lives.

Today, I dare to challenge a word problem allegedly given for the Nada Se-
nior High School entrance examination. Forgive me; I’m not sure whether
the question is authentic in its past questions, but without any doubt, it will
definitely be worth giving it a shot to improve my math skills.

Find (1) \(ab\) and (2) \(a + b\) given \(a^{2} + b^{2} = 28\)、\(a^{4} + b^{4} = 584\),
providing \(a>0\)、\(b>0\).

It’s not a piece of cake, but it is not a painstaking task either.

Here is my solution to the problem.

\((a^{2} + b^{2})^{2} = 28^{2}\)
\(a^{4} + 2a^{2}b^{2} + b^{4} = 784\)
\(2a^{2}b^{2} + 584 =784\)
\(2a^{2}b^{2} = 200\)
\(a^{2}b^{2} = 100\)
\((ab)^{2}=100\)
Providing \(a>0、b>0\), \(ab=10\)

\((a + b)^{2} = a^{2} + 2ab + b^{2} = 28 + 2 × 10 = 48\)
\(a + b = \pm 4\sqrt{3}\)
Providing \(a>0、b>0\), \(a + b = 4\sqrt{3}\)

Nada Senior High School is the school where no school regulations are
necessary because the students out there mind their manners, including
self-esteem and decency, voluntarily.

Remember, “Examine the content, not the bottle.” not to fall on your face
even in business.

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
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