Question

Tìm cac số a,b,c,d Thuộc N,biết: \(\dfrac{30}{43}=\dfrac{1}{a+\dfrac{1}{b+\dfrac{1}{c+\dfrac{1}{d}}}}\)

Answer 1

Có \(\dfrac{30}{43}=\dfrac{1}{\dfrac{43}{30}}=\dfrac{1}{1+\dfrac{13}{30}}=\dfrac{1}{1+\dfrac{1}{\dfrac{30}{13}}}=\dfrac{1}{1+\dfrac{1}{2+\dfrac{4}{13}}}=\dfrac{1}{1+\dfrac{1}{2+\dfrac{1}{\dfrac{13}{4}}}}=\dfrac{1}{1+\dfrac{1}{2+\dfrac{1}{3+\dfrac{1}{4}}}}\)
Vậy a=1; b=2 ; c=3 ; d=4

Answer 2

ta thấy : \(\dfrac{a}{b}\) = \(\dfrac{1}{\dfrac{b}{a}}\)

\(\Rightarrow\) \(\dfrac{30}{43}\) = \(\dfrac{1}{\dfrac{43}{30}}\)

= \(\dfrac{1}{1+\dfrac{13}{30}}\)

= \(\dfrac{1}{1+\dfrac{1}{\dfrac{30}{13}}}\)

= \(\dfrac{1}{1+\dfrac{1}{2+\dfrac{2}{15}}}\)

= \(\dfrac{1}{1+\dfrac{1}{2+\dfrac{1}{\dfrac{15}{2}}}}\)

=\(\dfrac{1}{1+\dfrac{1}{2+\dfrac{1}{7+\dfrac{1}{2}}}}\)

Vậy a = 1; b = 2; c = 7; d = 4