giúp với.
1.Complete the word.
p_ _ s_ _
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1. teacher
2. desk
3. ruler
4. pen
5. rubber
6. student
7. pencil case
8. calculator
9. book
10.chair
BE là tia phân giác của góc B nên \(\frac{AE}{BC}=\frac{AB}{BC}\Rightarrow\frac{AE}{AC}=\frac{AB}{BC+AB}\Rightarrow AE=\frac{bc}{a+c}\)
tương tự \(AE=\frac{bc}{a+b}\) \(\Rightarrow\frac{S_{AEF}}{S}=\frac{AE\cdot AF}{bc}=\frac{bc}{\left(a+c\right)\left(a+b\right)}\)
tương tự \(\frac{S_{BDF}}{S}=\frac{ac}{\left(b+c\right)\left(a+b\right)},\frac{S_{CDE}}{S}=\frac{ab}{\left(a+c\right)\left(c+b\right)}\)
bất đẳng thức cần chứng minh tương đương với \(\frac{S_{AEF}}{S}+\frac{S_{BDF}}{S}+\frac{S_{CDE}}{S}\ge\frac{3}{4}\)
\(\Leftrightarrow\frac{bc}{\left(a+b\right)\left(a+c\right)}+\frac{ca}{\left(b+c\right)\left(b+a\right)}+\frac{ab}{\left(c+a\right)\left(c+b\right)}\ge\frac{3}{4}\)
biến đổi tương đương bất đẳng thức trên ta được \(a^2b+a^2c+b^2c+b^2a+c^2a+c^2b\ge6abc\)
chia 2 vế cho abc ta được \(\left(\frac{a}{b}+\frac{b}{a}\right)+\left(\frac{b}{c}+\frac{c}{b}\right)+\left(\frac{a}{c}+\frac{c}{a}\right)\ge6\)
ta có \(\frac{a}{b}+\frac{b}{a}\ge2\)
áp dụng cho 3 cặp số suy ra điều phải chứng minh
dấu "=" xảy ra khi a=b=c hay tam giác ABC đều
1It is getting cold.
2He grew tired and hungry.
3The little girl got ready.
4She promised to be careful.
5Their neighbors are very friendly.
6We were driving along a lovely mountain road.
7We couldn't go further because the snow was too deep.
8The naughty child decided to take a short cut through the woods.
9She heard a loud noise when walking along a narrow path.
10When I saw her, she looked tired.
11It is a large house.
12It is a possible mission.
13I like anything beautiful.
14My parents are very strict.
15The piece of music sounds interesting.
10. Singapore is the second …………of the most………………. destination in Asia.
-parson
1.Complete the word.
person