Question

Bài 1: Tìm a , b , c , d \(\in\) N , biết :

\(\dfrac{30}{43}\) = \(\dfrac{1}{a+\dfrac{1}{b+\dfrac{1}{c+\dfrac{1}{d}}}}\)

Answer 1

\(\dfrac{30}{43}=\dfrac{1}{a+\dfrac{1}{b+\dfrac{1}{c+\dfrac{1}{d}}}}\)

\(\Leftrightarrow\dfrac{1}{\dfrac{43}{30}}=\dfrac{1}{a+\dfrac{1}{b+\dfrac{1}{c+\dfrac{1}{d}}}}\\ \Leftrightarrow\dfrac{1}{1+\dfrac{13}{30}}=\dfrac{1}{a+\dfrac{1}{b+\dfrac{1}{c+\dfrac{1}{d}}}}\\ \Leftrightarrow\dfrac{1}{1+\dfrac{1}{\dfrac{30}{13}}}=\dfrac{1}{a+\dfrac{1}{b+\dfrac{1}{c+\dfrac{1}{d}}}}\\ \Leftrightarrow\dfrac{1}{1+\dfrac{1}{2+\dfrac{4}{13}}}=\dfrac{1}{a+\dfrac{1}{b+\dfrac{1}{c+\dfrac{1}{d}}}}\)

\(\\ \Leftrightarrow\dfrac{1}{1+\dfrac{1}{2+\dfrac{1}{\dfrac{13}{4}}}}=\dfrac{1}{a+\dfrac{1}{b+\dfrac{1}{c+\dfrac{1}{d}}}}\\\Leftrightarrow\dfrac{1}{1+\dfrac{1}{2+\dfrac{1}{3+\dfrac{1}{4}}}}=\dfrac{1}{a+\dfrac{1}{b+\dfrac{1}{c+\dfrac{1}{d}}}}\)

\(\Rightarrow\left\{{}\begin{matrix}a=1\\b=2\\c=3\\d=4\end{matrix}\right.\)

Vậy............

Answer 2

bấm máy tính casio, ta được:

a=1; b=2; c=3; d=4