Question

[Ekachido Rika]

1. Cho \(\Delta ABC\)có \(\widehat{A}=180^o-3.\widehat{C}\). Khi đó \(\widehat{B}=\widehat{C}.k\). Vậy k bằng?

2. Cho \(x,y,z\ne0\) thỏa mãn \(\left(x+y\right)\left(y+z\right)\left(z+x\right)\ne0\)và \(\frac{xy}{x+y}=\frac{yz}{y+z}=\frac{zx}{z+x}\). Vậy ta có \(x-z=..?\)

Cả hình cả đại. Help me.

Answer 1

[zZz Cool Kid_new zZz]

Lật ngược lại:

\(\frac{xy}{x+y}=\frac{yz}{y+z}=\frac{zx}{z+x}\)

\(\Leftrightarrow\frac{x+y}{xy}=\frac{y+z}{yz}=\frac{z+x}{zx}\)

\(\Leftrightarrow\frac{1}{x}+\frac{1}{y}=\frac{1}{y}+\frac{1}{z}=\frac{1}{z}+\frac{1}{x}\)

\(\Rightarrow x=y=z\left(ez-see!\right)\)

\(\Rightarrow x-z=0\)