\(\dfrac{4}{x-3}=\dfrac{8}{y-6}=\dfrac{20}{z-15}\)

\(\Rightarrow\dfrac{x-3}{4}=\dfrac{y-6}{8}=\dfrac{z-15}{20}\)

\(\Rightarrow\dfrac{x}{4}-\dfrac{3}{4}=\dfrac{y}{8}-\dfrac{3}{4}=\dfrac{z}{20}-\dfrac{3}{4}\)

\(\Rightarrow\dfrac{x}{4}=\dfrac{y}{8}=\dfrac{z}{20}\)

Đặt: \(\dfrac{x}{4}=\dfrac{y}{8}=\dfrac{z}{20}=k\Leftrightarrow\left\{{}\begin{matrix}x=4k\\y=8k\\z=20k\end{matrix}\right.\)

Thay vào đk đề bài: \(640k^3=640\Leftrightarrow k=1\)

Vậy \(\left\{{}\begin{matrix}x=4\\y=8\\z=20\end{matrix}\right.\)

\(\frac{3}{3.6.9}+\frac{3}{6.9.12}+\frac{3}{9.12.15}+\frac{3}{12.15.18}=\frac{3}{6}\left(\frac{6}{3.6.9}+\frac{6}{6.9.12}+\frac{6}{9.12.15}+\frac{6}{12.15.18}\right)\)

= \(\frac{1}{2}\left(\frac{1}{3.6}-\frac{1}{6.9}+\frac{1}{6.9}-\frac{1}{9.12}+\frac{1}{9.12}-\frac{1}{12.15}+\frac{1}{12.15}-\frac{1}{15.18}\right)\)

\(=\frac{1}{2}\left(\frac{1}{3.6}-\frac{1}{15.18}\right)=\frac{1}{2}.\frac{14}{270}=\frac{7}{270}\)

\(\frac{4}{x-3}\)=\(\frac{8}{y-6}\)=\(\frac{20}{z-15}\)

=> \(\frac{x-3}{4}\)=\(\frac{y-6}{8}\)=\(\frac{z-15}{20}\)

=> \(\frac{x}{4}\)-\(\frac{3}{4}\)= \(\frac{y}{8}\)-\(\frac{6}{8}\)=\(\frac{z}{20}\)-\(\frac{15}{20}\)

=> \(\frac{x}{4}\)=\(\frac{y}{8}\)=\(\frac{z}{20}\)

Đặt \(\frac{x}{4}\)=\(\frac{y}{8}\)=\(\frac{z}{20}\)=k

\(\frac{x}{4}\)= k => x = 4 . k

\(\frac{y}{8}\)= k => y = 8 . k

\(\frac{z}{20}\)= k => z = 20 . k

Mà x.y.x = 640

(4k) . (8k) . (20k)= 640

640 . kmũ3 = 640

k mũ 3 = 640:640

k mũ 3 = 1

\(\frac{x}{4}\)= 1 => x = 4 . 1 = 4

\(\frac{y}{8}\)= 1 => y = 8 . 1 = 8

\(\frac{z}{20}\)= 1 => z = 20 . 1=20

Vậy x=4, y=8, z=20

k mình nha,đúng 100%

Ta có:\(\frac{4}{x-3}=\frac{8}{y-6}=\frac{20}{z-15}\)

=>\(\frac{x-3}{4}=\frac{y-6}{8}=\frac{z-15}{20}\)

=>\(\frac{x}{4}-\frac{3}{4}=\frac{y}{8}-\frac{6}{8}=\frac{z}{20}-\frac{15}{20}\)

=>\(\frac{x}{4}-\frac{3}{4}=\frac{y}{8}-\frac{3}{4}=\frac{z}{20}-\frac{3}{4}\)

=>\(\frac{x}{4}=\frac{y}{8}=\frac{z}{20}\)

Đặt \(\frac{x}{4}=\frac{y}{8}=\frac{z}{20}=k\Rightarrow x=4k,y=8k,z=20k\)

Thay vào đề ta có: xyz = 640

=> 4k.8k.20k = 640

=> 640k³ = 640

=> k³ = 1

=> k = 1

=> x = 4, y = 8, z = 20

Vậy...

B. 1/6 nhé!

B

b

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