Cho ba số thực dương a,b,c thỏa mãn ab+bc+ca=3.
Chứng minh rằng: \(\frac{a^3}{b^2+3 }+\frac{b^3}{c^2+3}+\frac{c^3}{a^2+3}\ge\frac{3}{4}\)
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đừng ai trả lời cái câu này em tui vừa nghịch đấy sorry nha
a. \(\left|2-x\right|=\left|2x-3\right|\)
\(\Rightarrow\orbr{\begin{cases}2-x=2x-3\\2-x=-2x+3\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{5}{3}\\x=1\end{cases}}\)
b. \(\left|x+3\right|=\left|5-x\right|\)
\(\Rightarrow\orbr{\begin{cases}x+3=5-x\\x+3=-5+x\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=1\\x=-8+x\left(vl\right)\end{cases}\Rightarrow x=1}\)
1. “ I’ll see you tomorrow’’->She said that she would see me the next day.
2. “ I saw her today’’->My brother said that he had seen her thay day.
3. “I don’t this film’’ => He said that he didn't that film.
4. “ We went swimming today’’ => Tom said that he went swimming that day
5. “ I’ll meet Mary on Sunday’’ => She said that she would see Mary
mik chỉ làm đến đây thôi xin lỗi
1. “ I’ll see you tomorrow’’-> She said that she would see me the day after.
2. “ I saw her today’’-> He said that he had seen her that day.
3. “I don’t this film’’-> She said that she didn't that film.
4. “ We went swimming today’’-> They said that they had gone swimming that day.
5. “ I’ll meet Mary on Sunday’’-> She said that she would meet Mary on Sunday.
6. “ Peter and Sue are getting married tomorrow’’-> He said that Peter and Sue were getting married the next day.
7. “I really this furniture’’-> She said that she really d that furniture.
8. “ I’m meeting them at four o’clock today’’-> He said that he was meeting them at four o' clock that day.
9. “ I live here with my parents’’-> He said he lived there with his parents.
10. “ Our new house is beautiful’’-> They said that their new house was beautiful.
11. “ I want to be a teacher of English’’-> She said that she wanted to be a teacher of English.
12. “ I can’t speak chinese’’-> She said that she couldn't speak Chinese.
13. “ My sister is now having a wonderful time in Nha Trang’’-> He said that his sister was now having a wonderful time in NT.
14. “ I’ll be very busy today’’-> He said that he would be very busy that day.
15. “ I must come to the meeting tomorrow’’-> She said that she had to come to the meeting tomorrow.
16.“ These roses are for you’’She told me-> She told to me that these roses were for me.
17. “ I’m going away tomorrow, mother’’-> He said to his mother that he was going away the following day.
Phân số chỉ 7 cái kẹo là
1-3/4=1/4 số kẹo còn lại sau khi cô cho Hạ
Số kẹo còn lại sau khi cô cho Hạ là
7:1/4=28 cái
Nếu cô chỉ cho Hạ 2/5 số kẹo còn lại sau khi cho Xuân thì khi đó số kẹo còn lại sau khi cho Hạ là
28+8=36 cái
Phân số chỉ 36 cái kẹo là
1-2/5=3/5 số kẹo còn lại sau khi cô cho Xuân
Số kẹo còn lại sau khi cô cho Xuân là
36:3/5=60 cái
Nếu cô chỉ cho Xuân 1/3 gói kẹo thì số kẹo còn lại sau khi cô cho Xuân khi đó là
60+4=64 cái
Phân số chỉ 64 cái kẹo là
1-1/3=2/3 gói kẹo
Số kẹo cô có là
64:2/3=96 cái
Ta có abcabc/abc = (abc×1000+abc)/abc
= abc×1000/abc + abc/abc = 1000 +1 =1001
Bg: Người em đã gấp được số con hạc là: 365 - 137 = 228 (con hạc)
Cả hai anh em đã gấp được số con hạc là: 365+ 228 = 593 (con hạc)
Đ/S: 593 con hạc
Vào thống kê hỏi đáp xem nhé. Bài này chỉ cần biểu diễn dưới dạng tổng bình phương là xong.
ta có \(\frac{a^3}{b^2+3}+\frac{b^3}{c^2+3}+\frac{c^3}{a^2+3}\ge\frac{3}{4}\) (***)
do ab+bc+ca=3 nên
VT (***)=\(\frac{a^3}{b^2+ab+bc+ca}+\frac{b^3}{c^2+ab+bc+ca}+\frac{c^3}{a^2+ab+bc+ca}\)
\(=\frac{a^3}{\left(b+c\right)\left(a+b\right)}+\frac{b^3}{\left(c+a\right)\left(b+c\right)}+\frac{c^3}{\left(a+b\right)\left(c+a\right)}\)
áp dụng bđt AM-GM ta có \(\frac{a^3}{\left(b+c\right)\left(c+a\right)}+\frac{b+c}{8}+\frac{a+b}{8}\ge\frac{3a}{4}\)
\(\Rightarrow\frac{a^3}{\left(b+c\right)\left(c+a\right)}\ge\frac{5a-2b-c}{8}\left(1\right)\)
chứng minh tương tự ta cũng được
\(\hept{\begin{cases}\frac{b^3}{\left(c+a\right)\left(a+b\right)}\ge\frac{5b-2c-a}{8}\left(2\right)\\\frac{c^3}{\left(a+b\right)\left(c+a\right)}\ge\frac{5c-2a-b}{8}\left(3\right)\end{cases}}\)
cộng theo vế với vế của (1),(2) và (3) ta được VT (***) \(\ge\frac{a+b+c}{4}\)
mặt khác ta dễ dàng chứng minh được \(a+b+c\ge\sqrt{3\left(ab+bc+ca\right)}=3\)
đẳng thức xảy ra khi a=b=c=1 (đpcm)