Question

số hữu tỉ \(\dfrac{43}{30}\)viết được dưới dạng 1+\(\dfrac{1}{x+\dfrac{1}{y+\dfrac{1}{z}}}\)tìm (x;y;z)

Answer 1

\(\dfrac{43}{30}=\dfrac{30+13}{30}=\dfrac{30}{30}+\dfrac{13}{30}=1+\dfrac{1}{\dfrac{30}{13}}\)

\(=1+\dfrac{1}{\dfrac{26+4}{13}}=1+\dfrac{1}{\dfrac{26}{13}+\dfrac{4}{13}}=1+\dfrac{1}{2+\dfrac{4}{13}}\)

\(=1+\dfrac{1}{2+\dfrac{1}{\dfrac{13}{4}}}=1+\dfrac{1}{2+\dfrac{1}{\dfrac{12+1}{4}}}=1+\dfrac{1}{2+\dfrac{1}{\dfrac{12}{4}+\dfrac{1}{4}}}=1+\dfrac{1}{2+\dfrac{1}{3+\dfrac{1}{4}}}\)

Vậy \(x=2;y-3;z=4\)