Question

Tìm x,y,z biết;

\(\frac{^{x^3}}{8}=\frac{^{y^3}}{64}=\frac{^{z^3}}{216}\) và \(^{x^2+y^2+z^2=14}\)

 

Answer 1

\(\frac{x^3}{8}=\frac{y^3}{64}=\frac{z^3}{216}\)=>\(\frac{x^3}{2^3}=\frac{y^3}{4^3}=\frac{z^3}{6^3}\)=>\(\frac{x}{2}=\frac{y}{4}=\frac{z}{6}\)

=>\(\frac{x^2}{2^2}=\frac{y^2}{4^2}=\frac{z^2}{6^2}\)=>\(\frac{x^2}{4}=\frac{y^2}{16}=\frac{z^2}{36}\)

Aps dụng t/c dãy tỉ số bằng nhau ta có:

\(\frac{x^2}{4}=\frac{y^2}{16}=\frac{z^2}{36}=\frac{x^2+y^2+z^2}{4+16+36}=\frac{14}{56}=\frac{1}{4}\)(vì x²+y²+z²=14)

=>\(\frac{x^2}{4}=\frac{1}{4}=>x^2=1=>x=1;x=-1\)

=>\(\frac{y^2}{16}=\frac{1}{4}=>y^2=4=>y=2;y=-2\)

=>\(\frac{z^2}{36}=\frac{1}{4}=>z^2=9=>z=3;z=-3\)

Vậy x=1; y=2 ; z=3

Hoặc x=-1 ;y=-2 ;z=-3