Question

tim x,y,z biet x³/8=y³/27=z³/125 va xyz=810

 

Answer 1

Ta có : \(\frac{x^3}{8}=\frac{y^3}{27}=\frac{z^3}{125}\)=> \(\frac{x^3}{2^3}=\frac{y^3}{3^3}=\frac{z^3}{5^3}\)=> \(\frac{x}{2}=\frac{y}{3}=\frac{z}{5}\)

Đặt \(\frac{x}{2}=\frac{y}{3}=\frac{z}{5}=k\)=> \(\hept{\begin{cases}x=2k\\y=3k\\z=5k\end{cases}}\)(*)

Khi đó, ta có: xyz = 810

hay 2k.3k.5k = 810

=> 30.k³ = 810

=> k³ = 810 : 30

=> k³ = 27

=> k = 3

Thay k = 3 vào * ta được:

x = 2 . 3 = 6

y = 3.3 = 9

z = 5 . 3 = 15

vậy ...