Question

x:y:z=3:4:5 và 2x\(^2\)+2y\(^2\)-3x\(^2\)=100

Answer 1

\(x:y:z=3:4:5\\ \Rightarrow\dfrac{x}{3}=\dfrac{y}{4}=\dfrac{z}{5}=k\)

 \(\Rightarrow\left\{{}\begin{matrix}x=3k\\y=4k\\z=5k\end{matrix}\right.\)

 \(2x^2+2y^2-3x^2=100\\ \Rightarrow2\left(3k\right)^2+2\left(4k\right)^2-3\left(3k\right)^2=100\\ \Rightarrow18k^2+32k^2-27k^2=100\\ \Rightarrow\left(18+32-27\right)k^2=100\\ \Rightarrow23k^2=100\\ \Rightarrow k^2=77\\ \Rightarrow k=\sqrt{77}\\ \left\{{}\begin{matrix}x=3\sqrt{77}\\y=4\sqrt{77}\\z=5\sqrt{77}\end{matrix}\right.\)

Answer 2

Theo mik thấy đề nó hơi sai sai