Question

cho \(\dfrac{x}{z}\)= \(\dfrac{z}{y}\). chứng minh rằng x² + z² / y²+z²=\(\dfrac{x}{y}\)

Answer 1

\(\dfrac{x}{z}=\dfrac{z}{y}\Rightarrow\dfrac{x.z}{z.y}=\dfrac{x}{y}=\dfrac{x^2}{z^2}=\dfrac{z^2}{y^2}=\dfrac{x^2+z^2}{y^2+z^2}\)

Answer 2

đăt \(\dfrac{x}{z}=\dfrac{z}{y}=k\)

=>\(\left\{{}\begin{matrix}x=zk\\z=yk\end{matrix}\right.\)=>\(\left\{{}\begin{matrix}x=yk^2\\z=yk\end{matrix}\right.\)

ta có :\(\dfrac{x}{y}=\dfrac{yk^2}{y}=k^2\left(1\right)\)

lại có \(\dfrac{x^2+z^2}{y^2+z^2}=\dfrac{y^2k^4+y^2k^2}{y^2+y^2k^2}=\dfrac{y^2k^2.\left(k^2+1\right)}{y^2.\left(1+k^2\right)}=k^2\left(2\right)\)

từ (1) và (2) => ĐPCM