Question

Tìm các số tự nhiên \(a,b\) biết: \(\dfrac{1719}{3976}=\dfrac{1}{2+\dfrac{1}{3+\dfrac{1}{5+\dfrac{1}{a+\dfrac{1}{b}}}}}\)

Answer 1

Lời giải:

\(\frac{1719}{3976}=\frac{1}{2+\frac{538}{1719}}=\frac{1}{2+\frac{1}{3+\frac{105}{538}}}=\frac{1}{2+\frac{1}{3+\frac{1}{5+\frac{13}{105}}}}=\frac{1}{2+\frac{1}{3+\frac{1}{5+\frac{1}{8+\frac{1}{13}}}}}\)

$\Rightarrow a=8; b=13$

Answer 2

\(\dfrac{1719}{3976}=\dfrac{1}{\dfrac{3976}{1719}}=\dfrac{1}{2+\dfrac{538}{1719}}=\dfrac{1}{2+\dfrac{1}{\dfrac{1719}{538}}}=\dfrac{1}{2+\dfrac{1}{3+\dfrac{105}{538}}}\)

\(=\dfrac{1}{2+\dfrac{1}{3+\dfrac{1}{\dfrac{538}{105}}}}=\dfrac{1}{2+\dfrac{1}{3+\dfrac{1}{5+\dfrac{13}{105}}}}=\dfrac{1}{2+\dfrac{1}{3+\dfrac{1}{5+\dfrac{1}{\dfrac{105}{13}}}}}\)

\(=\dfrac{1}{2+\dfrac{1}{3+\dfrac{1}{5+\dfrac{1}{8+\dfrac{1}{13}}}}}\)

Answer 3

1719​=17193976​1​=2+1719538​1​=2+5381719​1​1​=2+3+538105​1​1​

=12+13+1538105=12+13+15+13105=12+13+15+110513=2+3+105538​1​1​1​=2+3+5+10513​1​1​1​=2+3+5+13105​1​1​1​1​

=12+13+15+18+113=2+3+5+8+131​1​1​1​1​