a có xy<=(x+y)^2/4 
cm 
<=> 4xy<=x^2+y^2+2xy 
<=> (x^2+y^2-2xy)>=0 
<=>(x-y)^2>=0 (dúng0) 
áp dụng xy<=(x+y)^2/4=2^2/4=1 
daứ = xảy ra là x=y=1 
cach nđơn giản +dể hiểu

Ta có: \(3^{n-3}+5.3^{n-3}=486\)

\(\Rightarrow3^{n-3}\left(1+5\right)=486\)

\(\Rightarrow3^{n-3}.6=486\)

\(\Rightarrow3^{n-3}=486:6\)

\(\Rightarrow3^{n-3}=81\)

\(\Rightarrow3^{n-3}=3^4\)

\(\Rightarrow3^n=3^{4+3}\)

\(\Rightarrow3^n=3^7\)

\(\Rightarrow n=7\)

tíck mình nha 

1-1/2+2-2/3+3/4+4-1/4-3-1/3-2-1/2-1=(1-2+4-3-3-3)(1/2-2/3+3/4-1/4-1/3-1/2)=-6.(-1/6)=1

Ta có: \(1-\frac{1}{2}+2-\frac{2}{3}+\frac{3}{4}+4-\frac{1}{4}-3-\frac{1}{3}-2-\frac{1}{2}\)\(-1\)

\(=\left(1+2+4-3-2-1\right)+\left(-\frac{1}{2}-\frac{2}{3}+\frac{3}{4}-\frac{1}{4}-\frac{1}{3}-\frac{1}{2}\right)\)

\(=1+\left(\frac{-3}{2}\right)\)

\(=\frac{-1}{2}\)

a=a chứ = j

\(a.\frac{3}{28}\)

\(b.\frac{9}{5}\)

Bây giờ mình sẽ viết đầy đủ hơn nhé:

a) \(\frac{28^{15}.3^{17}}{84^{16}}=\frac{\left(28.3\right)^{15}.3^2}{\left(28.3\right)^{15}.84}=\frac{9}{84}=\frac{3}{28}\)

b)\(\frac{3^{10}+6^2}{5.3^8+20}=\frac{3^{10}+2^2.3^2}{5.3^8+20}=\frac{3^2.\left(3^8+2^2\right)}{5.\left(3^8+2^2\right)}\)\(=\frac{9}{5}\)