Discussion Forum

If $2+\frac{1}{x +\frac{1}{y+\frac{1}{z}}}=\frac{37}{13}$ where x, y, z are natural numbers, then x,y,z are:

Answer:

Explanation:

$2+\frac{1}{x +\frac{1}{y+\frac{1}{z}}}=\frac{37}{13}$
$=2 \frac{11}{13}=2+\frac{11}{13}$
$\Rightarrow\frac{1}{x +\frac{1}{y+\frac{1}{z}}}=\frac{11}{13}$
$\Rightarrow x+\frac{1}{y+\frac{1}{z}}=\frac{13}{11}$
$\Rightarrow x+\frac{1}{y+\frac{1}{z}}=1 +\frac{2}{11}$
$\Rightarrow x =1$, $y+\frac{1}{z}=\frac{11}{2}$
$=5\frac{1}{2}=5+\frac{1}{2}$
$\Rightarrow$ x =1, y = 5, z = 2