Đáp án:
Giải thích các bước giải:
1/ Ta có: $\frac{x}{2}=\frac{y}{3}=\frac{z}{5}$
⇒ $\frac{x^2}{4}=\frac{y^2}{9}=\frac{z^2}{25}=\frac{3y^2}{27}=\frac{x^2+3y^2-x^2}{4+27-25}=\frac{150}{6}=25$
⇒ $\left\{\begin{matrix}x^2=100 &\\y^2=225& \\ z^2=625 & \end{matrix}\right.$
⇒ $\left\{\begin{matrix}x=10 &\\y=15& \\ z=25 & \end{matrix}\right.$
2/
a/ $\frac{x}{3}=\frac{y}{5}=\frac{z}{6}=\frac{x+y+z}{3+5+6}=\frac{56}{14}=4$
⇒ $\left\{\begin{matrix}x=12 &\\y=20& \\ z=24 & \end{matrix}\right.$
b/ $\frac{x}{3}=\frac{y}{5}=\frac{z}{6}=\frac{2y}{10}=\frac{3z}{18}=\frac{x-2y+3z}{3-10+18}=\frac{-33}{11}=-3$
⇒ $\left\{\begin{matrix}x=-9 &\\y=-15& \\ z=-18 & \end{matrix}\right.$
c/ Ta có: $\frac{x}{3}=\frac{y}{5}=\frac{z}{6}$ (1)
⇒ $\frac{x^3}{27}=\frac{x}{3}.\frac{y}{5}.\frac{z}{6}=\frac{xyz}{3.5.6}=\frac{720}{90}=8$
⇒ $x^3=216$
⇒ $x=6$
Thay x vào (1) ta được: $\frac{y}{5}=\frac{z}{6}=\frac{6}{3}=2$
⇒ $\left \{ {{y=10} \atop {z=12}} \right.$
Vậy $x=6, y=10, z=12$
d/ $\frac{x}{3}=\frac{y}{5}=\frac{z}{6}$
⇒ $\frac{x^2}{9}=\frac{y^2}{25}=\frac{z^2}{36}=\frac{4y^2}{100}=\frac{2z^2}{72}=\frac{x^2-4y^2+2z^2}{9-100+72}=\frac{-475}{-19}=25$
⇒ $\left\{\begin{matrix}x^2=225 &\\y^2=625& \\ z^2=900 & \end{matrix}\right.$
⇒ $\left\{\begin{matrix}x=15 &\\y=25& \\ z=30 & \end{matrix}\right.$
Chúc bạn học tốt !!