Question

Tìm các số a,b,c,d thuộc N:

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

Answer 1

\(\frac{30}{43}=\frac{1}{\frac{43}{30}}=\frac{1}{1+\frac{13}{30}}=\frac{1}{1+\frac{1}{\frac{30}{13}}}=\frac{1}{1+\frac{1}{2+\frac{4}{13}}}=\frac{1}{1+\frac{1}{2+\frac{1}{\frac{13}{4}}}}=\frac{1}{1+\frac{1}{2+\frac{1}{3+\frac{1}{4}}}}\)

vậy (a;b;c;d)=(1;2;3;4)

Answer 2

\(\frac{30}{43}=\frac{1}{\frac{43}{30}}=\frac{1}{1+\frac{13}{30}}=\frac{1}{1+\frac{1}{\frac{30}{13}}}=\frac{1}{1+\frac{1}{2+\frac{4}{13}}}=\frac{1}{1+\frac{1}{2+\frac{1}{\frac{13}{4}}}}=\frac{1}{1+\frac{1}{2+\frac{1}{3+\frac{1}{4}}}}\)

Vậy a=1 ; b=2 ; c=3 ; d=4

Answer 3

https://olm.vn/images/myolm.png

Answer 4

Ta có:

\(\frac{30}{43}=\frac{1}{\frac{43}{30}}=\frac{1}{1+\frac{13}{30}}=\frac{1}{1+\frac{1}{\frac{30}{13}}}=\frac{1}{1+\frac{1}{2+\frac{4}{13}}}+\frac{1}{1+\frac{1}{2+\frac{1}{\frac{13}{4}}}}=\frac{1}{1+\frac{1}{2+\frac{1}{3+\frac{1}{4}}}}\) (*)

Từ (*),ta  lại có: \(\frac{1}{a+\frac{1}{b+\frac{1}{c+\frac{1}{d}}}}=\frac{1}{1+\frac{1}{2+\frac{1}{3+\frac{1}{4+1}}}}\Rightarrow a=1,b=2,c=3,d=4\)

Vậy ...

Answer 5

ai choi bang bang 2 ket ban voi minh