Question

1) Tìm $x,y,z$ biết $3x=4y;5y=6z$ và $xyz=30$

 

Answer 1

3x=4y

=>\(\dfrac{x}{4}=\dfrac{y}{3}\)

=>\(\dfrac{x}{8}=\dfrac{y}{6}\)(1)

5y=6z

=>\(\dfrac{y}{6}=\dfrac{z}{5}\)(2)

Từ (1),(2) suy ra \(\dfrac{x}{8}=\dfrac{y}{6}=\dfrac{z}{5}\)

Đặt \(\dfrac{x}{8}=\dfrac{y}{6}=\dfrac{z}{5}=k\)

=>x=8k; y=6k; z=5k

xyz=30

=>\(8k\cdot6k\cdot5k=30\)

=>\(k^3=\dfrac{1}{8}\)

=>\(k=\dfrac{1}{2}\)

=>\(\left\{{}\begin{matrix}x=8k=8\cdot\dfrac{1}{2}=4\\y=6k=6\cdot\dfrac{1}{2}=3\\z=5k=5\cdot\dfrac{1}{2}=\dfrac{5}{2}\end{matrix}\right.\)