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1st paragragh
Our childhood has many adorable, even fanciful, desires. I also had a dream, although my dream is a bit weird, but I also want to share it with everyone. In the future, when I grow up, I want to be a YouTuber. I have also expressed my dream to everyone around but most of them do not agree, the only one who agrees is a friend who forgot on my internet, but I did not give up, I decided to go later. follow my own dream. When I watch on TV, there are many good game players, and loved by many people, I also want to be like that, so I also want to be a YouTube channel. I don't want to be only a Vietnamese Youtubers, but I also want to reach out further by speaking English. In my channel, I will speak English, and at the same time speak English about Vietnamese customs and habits, and beautiful Vietnamese hunchbacks. Although my dream is very unusual, please accept it.
2nd paragragh
Each of us has ambitions to travel around the world to see interesting and beatiful natural wonders. I once had a desire to come to Japan to see Mount Fuji, one of the famous symbols of Japan. The best time of the year to see Mount Fuji is in the spring. At that time, Japan's flower, cherry blossom, will bloom, this is the most appropriate time for tourists who like to see the cherry blossoms. There are many elderly who want to climb this mountain to prove their health. Today, the mountain still attract foreign tourists. Proving that Mount Fuji still holds an improtance for this land. To admire the sunrise, the rare beauty from the top of the mountain you have to climb all night. If you can watch the sunrise from Mount Fuji, it will be an extremely valuable experience for you when coming to Japan. I really hope ij the future, I will go to Japan to see this wonderful mountian.
3rd Paragragh
The last ambition of my life, also my biggest dream, maybe people won't understand, but it means a lot to me. I have a friend, whom I love a lot, is Lien Ai, my best friend. I have know him since the beginning of the new year, and we met in a very special way, we met by online, we could talk through text messagers, we didn't even get to see each other, and not hear each other's real voices, which make me very sad.. We used to be very close, but now we are quiet distant . Lien Ai is the person who I love and trust most, and most especially, he is the first person to agree my dream of becoming a Youtuber, something my family, and everyone else around think it is crazy. Tha's why I want to meet him. But this seems very impossible, we are almost in the two parts of the country, so perhaps this ambition of mine will not able to become true. Even so, I stll want this wish, this ambition of mine to come true. Thanks for reading, have a nice day!
Áp dụng bất đẳng thức Holder ta có:
\(\left(\dfrac{a}{\sqrt{a^2+8bc}}+\dfrac{b}{\sqrt{b^2+8ca}}+\dfrac{c}{\sqrt{c^2+8ab}}\right)\left(\dfrac{a}{\sqrt{a^2+8bc}}+\dfrac{b}{\sqrt{b^2+8ca}}+\dfrac{c}{\sqrt{c^2+8ab}}\right)\left(a\left(a^2+8bc\right)+b\left(b^2+8ca\right)+c\left(c^2+8ab\right)\right)\ge\left(a+b+c\right)^3\).
Do đó ta chỉ cần chứng minh \(\left(a+b+c\right)^3\ge a\left(a^2+8bc\right)+b\left(b^2+8ca\right)+c\left(c^2+8ab\right)\Leftrightarrow3\left(a+b\right)\left(b+c\right)\left(c+a\right)\ge24abc\Leftrightarrow\left(a+b\right)\left(b+c\right)\left(c+a\right)\ge8abc\). Đây là một bđt rất quen thuộc
Không Holder thì Svacxo nha :v
Áp dụng BĐT Svacxo ta có :
\(\dfrac{a^2}{a\sqrt{a^2+8bc}}+\dfrac{b^2}{b\sqrt{b^2+8ac}}+\dfrac{c^2}{c\sqrt{c^2+8ab}}\ge\dfrac{\left(a+b+c\right)^2}{a\sqrt{a^2+8bc}+b\sqrt{b^2+8ac}+c\sqrt{c^2+8ab}}\)
Ta có sẽ đi chứng minh :
\(a\sqrt{a^2+8bc}+b\sqrt{b^2+8ac}+c\sqrt{c^2+8ab}\le\left(a+b+c\right)^2\)
Thật vậy theo Bunhiacopxki có :
\(a\sqrt{a^2+8bc}+b\sqrt{b^2+8ac}+c\sqrt{c^2+8ab}=\sqrt{a}\sqrt{a^3+8abc}+\sqrt{b}\sqrt{b^3+8abc}+\sqrt{c}\sqrt{c^3+8abc}\)
\(\le\sqrt{\left(a+b+c\right)\left(a^3+b^3+c^3+24abc\right)}\)
Ta lại đi chứng minh :
\(a^3+b^3+c^3+24abc\le\left(a+b+c\right)^3\)
\(\Leftrightarrow24abc\le3\left(a+b\right)\left(b+c\right)\left(c+a\right)\) ( Đây là BĐT đúng )
Do đó nhân vào ta có đpcm.
Em cảm ơn cô ạ , các đề thi thử trên hoc24.vn hay lắm ạ
Spoil tí vòng 1 với vòng 2 khá là dễ ăn, full điểm bình thường nên các bạn làm bài hết sức cẩn thận để tránh những sai sót đáng tiếc.
Cố gắng để làm đề trùm - đề vòng 3 (vòng 3 có **** đấy, cẩn thận :) :v
ĐK: \(0\le x\le1\).
Ta có:
với \(0\le x\le1\)thì \(0\le1-x\le1\Leftrightarrow\sqrt{1-x}\left(1-\sqrt{1-x}\right)\ge0\Leftrightarrow\sqrt{1-x}\ge1-x\)
do đó \(x+\sqrt{1-x}\ge x+1-x=1\Rightarrow\sqrt{x+\sqrt{1-x}}\ge1\).
Do đó để phương trình đã cho có nghiệm thì:
\(\hept{\begin{cases}\sqrt{x}=0\\x+\sqrt{1-x}=1\end{cases}}\Leftrightarrow x=0\left(tm\right)\).
Sorry so much :((
thao nào em cứ thấy nó sao sao ý tự dưng chưa hết hạn nộp đã công bố ai nhất nhì , ba =)))