Question

x/5=y/7=z/3 và X^2 + y^2 - z^2 =585 Tìm x,y,z

Answer 1

x/5 = y/7 = z/3 =>(x/5)^2= (y/7)^2 = (z/3)^2 hay x^2/25 = y^2/49 =z^2 /9  

x^2/25 = y^2/49 =z^2 /9 = (x^2 + y^2 - z^2) /(25+49 -9)=585/65 =9=3^2  

=> (x/5)^2=3^2 =>x/5 =+-3 =>x=+-15  

(y/7)^2=3^2 =>y/7 =+-3 =>y=+-21  

(z/3)^2 =3^2 =>z/3 =+-3 =>z=+-9  

vậy có 2 cặp (x;y;z) là: (15;21;9) và (-15;-21;-9)

Answer 2

\(\frac{x}{5}=\frac{y}{7}=\frac{z}{3}=\frac{x^2}{25}=\frac{y^2}{49}=\frac{z^2}{9}=\frac{585}{65}=9\)

\(\Rightarrow\frac{x^2}{25}=9\Rightarrow x^2=225\Rightarrow x=15hoặc-15\)

\(\frac{y^2}{49}=9\Rightarrow y^2=441\Rightarrow y=21hoặc-21\)

\(\frac{z^2}{9}=9\Rightarrow z^2=81\Rightarrow z=9\)