Question

Tìm x,y,z biết :

\(\dfrac{x}{3}=\dfrac{y}{7}=\dfrac{z}{2}\) và 2x² + y² + 3z² = 316

Answer 1

\(\dfrac{x}{3}=\dfrac{y}{7}=\dfrac{z}{2}\)

\(\Rightarrow\dfrac{x^2}{9}=\dfrac{y^2}{49}=\dfrac{z^2}{4}\)

\(\Rightarrow\dfrac{2x^2}{18}=\dfrac{y^2}{49}=\dfrac{3z^2}{12}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có:

\(\dfrac{2x^2}{18}=\dfrac{y^2}{49}=\dfrac{3z^2}{12}=\dfrac{2x^2+y^2+3z^2}{18+49+12}=\dfrac{316}{79}=4\)

\(\Rightarrow\left\{{}\begin{matrix}x^2=4.18:2=36\\y^2=4.49=196\\z^2=4.12:3=16\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=6\\y=14\\z=4\end{matrix}\right.\\\left\{{}\begin{matrix}x=-6\\y=-14\\z=-4\end{matrix}\right.\end{matrix}\right.\)