Writing about the benefits of an invention ( about 100-150 words)

2 bình luận về “Writing about the benefits of an invention ( about 100-150 words)”

1. The invention of the cellphone dramatically changed the way of human history. Being able to interact with people, particularly far away, just through texting t made my life easier. With my cell phone, I will be able to tell or text family and friends from the house whenever I need. That helps me keep lifelong friendships and be in short touch with my home, both of which I highly measure. However, I would admit that this characteristic of texting does have the power to get away from actual human interaction. It’s often easier to text someone, particularly if we just have one simple question to ask them. I frequently find myself texting things to someone who is just experiencing their doors down from me because I am too lazy to speak to them.

   $#Nobita$

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2. We will apply the AM-GM inequality to the terms $a^8$, $b^8$, and $c^8$, which yields:

   $$a^8 + b^8 + c^8 \ge 3\sqrt[3]{(a^8)(b^8)(c^8)} = 3a^{\frac{8}{3}}b^{\frac{8}{3}}c^{\frac{8}{3}}$$

   Using the fact that $a+b+c=3$, we can use the AM-GM inequality to obtain:

   $$abc \le \left(\frac{a+b+c}{3}\right)^3 = 1$$

   Therefore, we have:

   $$a^{\frac{8}{3}}b^{\frac{8}{3}}c^{\frac{8}{3}} \le 1$$

   Substituting this inequality into the first inequality, we get:

   $$a^8 + b^8 + c^8 \ge 3a^{\frac{8}{3}}b^{\frac{8}{3}}c^{\frac{8}{3}} \ge 3$$

   Using the AM-GM inequality again, we have:

   $$(a-1)(b-1)(c-1) \le \left(\frac{(a-1)+(b-1)+(c-1)}{3}\right)^3 = \frac{8}{27}$$

   Therefore, we can write:

   $$S = a^8 + b^8 + c^8 + 2(a-1)(b-1)(c-1) \ge 3 + 2\cdot\frac{8}{27} = \frac{67}{9}$$

   To find the minimum value of $S$, we need to find the values of $a$, $b$, and $c$ that satisfy the equality conditions for the AM-GM inequalities used above. This occurs when $a=b=c=1$, which satisfies $a+b+c=3$ and $abc=1$. Substituting these values into the expression for $S$, we obtain:

   $$S = 3 + 2(0) = 3$$

   Therefore, the minimum value of the expression $S$ is $3$.

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