Bài làm:

Benefits of a smartphone:

- Nowadays, most young people have a smartphone. It has become a must-have device that serves many purposes in their daily life.

- First, a smartphone is used for communication. We can instantly make phone calls, send and receive messages anywhere, anytime because it's portable. Using a smartphone is more convenient than using a telephone and faster than writing a letter.

- Second, we can use a smartphone for entertainment. Listening to music, watching films, and playing games are some interesting functions. Besides, we can also use it to take photos and record videos to keep our happy moments.

- Finally, we can easily find the information we need via a smartphone. Once it is connected to a wireless or mobile data network, we can surf the web, and even use maps to look for places.

Benefits of a digital camera:

- Digital cameras bring a new level of enjoyment to picture taking and have numerous advantages. First, they are portable: light, small and not bulky. Besides, they are also convenient. It takes a short time to view and delete photos. Morever, it becomes easier than ever to store and transfer photos to a computer. Last but not least, they are economical. You do not have to spend any money on film, which is great.

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\(1,\left(\frac{\left(x+1\right)^2.\left(y+1\right)^2}{\left(x+1\right)^2}+\frac{\left(x+1\right)^2\left(y+1\right)^2}{\left(y+1\right)^2}\right)\left(xy+1\right)\ge\left(x+1\right)^2\left(y+1\right)^2\)

\(\left[\left(y+1\right)^2+\left(x+1\right)^2\right]\left(xy+1\right)\ge\left(xy+y+x+1\right)^2\)

\(\left(y^2+2y+1+x^2+2x+1\right)\left(xy+1\right)\ge\left(xy+y+x+1\right)^2\)

\(\left(y^2+2y+1+x^2+2x+1\right)\left(xy+1\right)-\left(xy+y+x+1\right)^2\ge0\)

\(\left(y^2+2y+1+x^2+2x+1\right)\left(xy+1\right)-\left(x^2+2x+1\right)\left(y^2+2y+1\right)\ge0\)

\(xy\left(x-1\right)^2+\left(xy-1\right)^2\ge0\)

\(< =>BĐT\)luôn đúng

dấu "=" xảy ra khi \(x=y=1\)

mình ko chắc đã đúngg đâu

ĐK: \(x^2-3y^2+30\ge0\).

Phương trình thứ nhất tương đương với: 

\(\left(x-y+3\right)\left(x+2y-1\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=y-3\\x=1-2y\end{cases}}\)

Với \(x=y-3\)thế vào phương trình thứ hai ta được: 

\(\sqrt{\left(y-3\right)^2-3y^2+30}+y-3-2y-5=0\)

\(\Leftrightarrow\sqrt{-2y^2-6y+39}=y+8\)

\(\Rightarrow-2y^2-6y+39=y^2+16y+64\)

\(\Leftrightarrow\orbr{\begin{cases}y=\frac{-11+\sqrt{46}}{3}\Rightarrow x=\frac{-20+\sqrt{46}}{3}\\y=\frac{-11-\sqrt{46}}{3}\Rightarrow x=\frac{-20-\sqrt{46}}{3}\end{cases}}\)

Thử lại thỏa mãn. 

Với \(x=1-2y\)làm tương tự, thu được thêm một nghiệm là: \(x=\frac{17-2\sqrt{61}}{5},y=\frac{-6+\sqrt{61}}{5}\).

Trả lời :

B. Sydeny là thành phố của nước Úc

ĐK: \(1-sinx\ne0\Leftrightarrow x\ne\frac{\pi}{2}+l2\pi\left(l\inℤ\right)\).

\(\frac{cos3x}{1-sinx}=0\)

\(\Rightarrow cos3x=0\)

\(\Leftrightarrow3x=\frac{\pi}{2}+k\pi\left(k\inℤ\right)\)

\(\Leftrightarrow x=\frac{\pi}{6}+\frac{k\pi}{3}\left(k\inℤ\right)\)

Đối chiếu điều kiện: 

\(\frac{\pi}{6}+\frac{k\pi}{3}=\frac{\pi}{2}+l\pi\Leftrightarrow\frac{1}{3}=\frac{k}{3}-l\Leftrightarrow k=3l+1\).

Vậy nghiệm phương trình là \(x=\frac{\pi}{6}+\frac{k\pi}{3}\)với \(k\inℤ,k\ne3l+1\left(l\inℤ\right)\).

bạn vẽ trục số ra thì ra đc 

\(-1\le x\le2\)

kết luận.......

bổ sung :

\(ĐKXĐ:x\ne2\)

\(< =>-1\le x< 2\)

From: Khanh Van

To: Heart to Heart Volunteer Organizing Committee

Mình xin lỗi, mình làm nhầm.