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ÉT Ô ÉT

2/-9<8/-9

-2/5<-3/4

\(a.\dfrac{2}{-9}và\dfrac{8}{-9}\)

Ta có: \(\dfrac{-2}{9}và\dfrac{-8}{9}\)

vì -2 > -8 

-> \(\dfrac{2}{-9}>\dfrac{8}{-9}\)

\(b.\dfrac{-2}{5}và\dfrac{-3}{4}\)

Ta có: \(\dfrac{-2}{5}=\dfrac{-8}{20};\dfrac{-3}{4}=\dfrac{-15}{20}\)

Vì -8 > -15

=> \(\dfrac{-2}{5}>\dfrac{-3}{4}\)

\(\left(2\sqrt{2}+\sqrt{3}\right)^2=11+4\sqrt{6};9^2=81=11+70\\ \left(4\sqrt{6}\right)^2=96< 70^2=4900\\ \Leftrightarrow11+4\sqrt{6}< 11+70\\ \Leftrightarrow2\sqrt{2}+\sqrt{3}< 9\)

Ta có :

1⁹ < 8⁹

2⁹ < 8⁹

.......

8⁹ = 8⁹

=> 1⁹ + 2⁹ + .... + 8⁹ < 8⁹ + 8⁹ + .... + 8⁹ = 8.8⁹ = 8¹⁰ < 9¹⁰ ( số trung gian là 8¹⁰ )

=> 1⁹ + 2⁹ + .... + 8⁹ < 9¹⁰ 

Ta có:

M=33669:(9×3)=33669:9:3=3741:3=1247

N=33669:9+3=3741+3=3744.

Mà 1247 < 3744

Do đó: 336699:(9×3) < 336699:9+3.

Hay M < N.

Đáp án A

Ta có : \(\frac{2^9}{3^{2010}}:\frac{3^9}{2^{2010}}=\frac{2^{2019}}{3^{2019}}=\left(\frac{2}{3}\right)^{2019}< 1^{2019}=1\)

Vì \(\frac{2^9}{3^{2010}}:\frac{3^9}{2^{2010}}< 1\)

=> \(\frac{2^9}{3^{2010}}< \frac{3^9}{2^{2010}}\)

       Bài làm :

Cách 1:

Ta có :

 \(\frac{2^9}{3^{2010}}\div\frac{3^9}{2^{2010}}=\frac{2^9.2^{2010}}{3^{2010}.3^9}=\frac{2^{2019}}{3^{2019}}=\left(\frac{2}{3}\right)^{2019}< 1\)

 \(\Rightarrow\frac{2^9}{3^{2010}}< \frac{3^9}{2^{2010}}\)

Cách 2 :

Nhận thấy :

\(\Rightarrow\frac{2^9}{3^{2010}}< \frac{3^9}{2^{2010}}\)