[Đại số 8]bài toán chứng minh

Q

quynhphamdq

T

transformers123

Xét:

$VT = (1+\dfrac{x-y}{x+y})(1+\dfrac{y-z}{y+z})(1+\dfrac{z-x}{z+x})$

$\iff VT=\dfrac{x+y+x-y}{x+y}.\dfrac{y+z+y-z}{y+z}.\dfrac{z+x+z-x}{z+x}$

$\iff VT=\dfrac{8xyz}{(x+y)(y+z)(z+x)} \bigstar_1$

Xét tiếp:

$VP=(1-\dfrac{x-y}{x+y})(1-\dfrac{y-z}{y+z})(1-\dfrac{z-x}{z+x})$

$\iff VP=\dfrac{x+y-x+y}{x+y}.\dfrac{y+z-y+z}{y+z}.\dfrac{z+x-z+x}{z+x}$

$\iff VP=\dfrac{8xyz}{(x+y)(y+z)(z+x)} \bigstar_2$

Từ $\bigstar_1$ và $\bigstar_2$, ta có ngay $\mathfrak{DPCM}$
 
Last edited by a moderator:
You must log in or register to reply here.
Top Bottom