Ta có :

9³⁴ - 27²² + 81¹⁶

= ( 3² )⁶⁴ - ( 3³ )²² + ( 3⁴ )¹⁶

= 3⁶⁸ - 3⁶⁶ + 3⁶⁴

= 3⁶⁸ . ( 3⁴ - 3² + 1 )

= 3⁶⁸ . 73 

= 3⁶⁶ . ( 3² . 73 )

= 3⁶⁶ . 657 \(⋮\)657

Vậy ...

SKT_NTT .Dòng thứ 3 từ trên xuống có vấn đề.

a) Ta có: \(2x=3y\Rightarrow\frac{x}{3}=\frac{y}{2}\)

               \(3y=5z\Rightarrow\frac{y}{5}=\frac{z}{3}\)

\(\Rightarrow\frac{x}{15}=\frac{y}{10}=\frac{z}{6}=\frac{x-2y+3z}{15-2.10+3.6}=\frac{65}{13}=5\)

\(\Rightarrow x=5.15=75\)

      \(y=5.10=50\)

      \(z=5.6=30\)

b) Ta có: \(\frac{x}{5}=\frac{y}{3};\frac{y}{7}=\frac{z}{4}\Rightarrow\frac{x}{35}=\frac{y}{21}=\frac{z}{12}=\frac{x+y-z}{35+21-12}=\frac{132}{44}=3\)

\(\Rightarrow x=3.35=105\)

      \(y=3.21=63\)

      \(z=3.12=36\)

c) Gọi \(\frac{x}{4}=\frac{y}{7}=k\)

\(\Rightarrow x=4k;y=7k\)

\(\Rightarrow x.y=4k.7k=28k^2=112\)

\(\Rightarrow k^2=112:28=4\)

\(\Rightarrow k=\pm2\)

\(\Rightarrow x=\pm2.4=\pm8\)

     \(y=\pm2.7=\pm14\)

đặt x/2 = y/3 = z/5 = k

=> x = 2k ; y = 3k ; z = 5k

vì xyz = 810

hay 2k . 3k . 5k = 810

30k³ = 810

k³ = 27

=> k = 3

Từ đó suy ra : a = 6 ; b = 9 ; z = 15

Vậy ...

Gọi \(\frac{x}{2}=\frac{y}{3}=\frac{z}{5}=k\)

\(\Rightarrow x=2k;y=3k;z=5k\)

\(\Rightarrow x.y.z=2k.3k.5k=810\)

\(\Rightarrow30k^3=810\)

\(\Rightarrow k^3=27\)

\(\Rightarrow k=3\)

\(\Rightarrow x=3.2=6\)

      \(y=3.3=9\)

      \(z=3.5=15\)

Vậy x = 6; y = 9; z = 15