a, Ta có: \(11x=8y\Rightarrow\dfrac{x}{8}=\dfrac{y}{11}\) (1)
\(7y=11z\Rightarrow\dfrac{y}{11}=\dfrac{z}{7}\) (2)
Từ (1) và (2) \(\Rightarrow\dfrac{x}{8}=\dfrac{y}{11}=\dfrac{z}{7}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có: \(\dfrac{x}{8}=\dfrac{y}{11}=\dfrac{z}{7}=\dfrac{10z}{70}=\dfrac{x+y-10z}{8+11-70}=\dfrac{-102}{-51}=2\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{x}{8}=2\\\dfrac{y}{11}=2\\\dfrac{z}{7}=2\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=2.8\\y=2.11\\z=2.7\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=16\\y=22\\z=14\end{matrix}\right.\)
Vậy x = 16, y = 22, z = 14.
b: x/4=2y/5=5z/6
nên 15x=24y=50z
=>x/40=y/25=z/12
Đặt x/40=y/25=z/12=k
=>x=40k; y=25k; z=12k
Ta có: x^2-3y^2+2z^2=325
=>1600k^2-3*625k^2+2*144k^2=325
=>k^2=25
TH1: k=5
=>x=200; y=125; z=60
TH2: k=-5
=>x=-200; y=-125; z=-60
