Question

[ngọc hân]

giải hệ phương trình 

\(\left\{{}\begin{matrix}\dfrac{x+y}{xy}=\dfrac{3}{8}\\\dfrac{y+x}{yz}=\dfrac{3}{4}\\\dfrac{x+z}{xz}=\dfrac{5}{6}\end{matrix}\right.\)

Answer 1

[Akai Haruma]

Lời giải:
HPT \(\Leftrightarrow \left\{\begin{matrix} \frac{1}{x}+\frac{1}{y}=\frac{3}{8}\\ \frac{1}{y}+\frac{1}{z}=\frac{3}{4}\\ \frac{1}{z}+\frac{1}{x}=\frac{5}{6}\end{matrix}\right.\Rightarrow 2(\frac{1}{x}+\frac{1}{y}+\frac{1}{z})=\frac{3}{8}+\frac{3}{4}+\frac{5}{6}\)

\(\Leftrightarrow \frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{47}{48}\)

\(\Rightarrow \left\{\begin{matrix} \frac{1}{z}=\frac{47}{48}-\frac{3}{8}\\ \frac{1}{x}=\frac{47}{48}-\frac{3}{4}\\ \frac{1}{y}=\frac{47}{48}-\frac{5}{6}\end{matrix}\right.\Leftrightarrow \left\{\begin{matrix} x=\frac{48}{29}\\ y=\frac{48}{11}\\ z=\frac{48}{7}\end{matrix}\right.\)