Vì y-x = 5 ⇒ y = 5+x
Ta có:
$\frac{4}{x}$ + $\frac{4}{y}$ = $\frac{2}{3}$
⇔ 4. ($\frac{1}{x}$ + $\frac{1}{y}$ ) = $\frac{2}{3}$
⇔ $\frac{1}{x}$ + $\frac{1}{y}$ = $\frac{1}{6}$
⇔$\frac{x+y}{xy}$ = $\frac{1}{6}$
⇔ $\frac{x+x+5}{x(x+5)}$ = $\frac{1}{6}$
⇔ $\frac{2x+5}{x(x+5)}$ = $\frac{1}{6}$
⇔ x.(x+5) = 6. (2x+5)
⇔ x² + 5x = 12x + 30
⇔ x² + 5x - 12x - 30 = 0
⇔ x² - 7x - 30 = 0
⇔ x² + 3x - 10x - 30 = 0
⇔ x.(x+3) - 10.(x+3) = 0
⇔ (x+3).(x-10) = 0
⇔ \(\left[ \begin{array}{l}x+3 = 0 \\x-10 = 0\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x=-3\\x=10\end{array} \right.\)
