Câu hỏi của Hoàng Tranh Tử

Question

Cho dãy tỉ số bằng nhau: $\frac{x}{2017}=\frac{y}{2016}=\frac{z}{2015}$. Chứng minh rằng: 2(z-y) mũ 2=(z-x)(z-y)

Nguyễn Đăng Nhân · Accepted Answer

$2\left(x-y\right)^2=\left(z-x\right)\left(z-y\right)\Leftrightarrow\frac{2\left(x-y\right)^2}{\left(z-x\right)\left(z-y\right)}=1$

$\frac{2\left(z-y\right)^2}{\left(z-x\right)\left(z-y\right)}=\frac{\left(x-y\right)^2}{z\left(x-y\right)}=\frac{x-y}{z}\Rightarrow x-y=z$

Câu trả lời:

$2\left(x-y\right)^2=\left(z-x\right)\left(z-y\right)\Leftrightarrow\frac{2\left(x-y\right)^2}{\left(z-x\right)\left(z-y\right)}=1$

$\frac{2\left(z-y\right)^2}{\left(z-x\right)\left(z-y\right)}=\frac{\left(x-y\right)^2}{z\left(x-y\right)}=\frac{x-y}{z}\Rightarrow x-y=z$