Cho \(\dfrac{\overline{abc}}{a+\overline{bc}}=\dfrac{\overline{bca}}{b+\overline{ca}}\)
CM: \(\dfrac{a}{\overline{bc}}=\dfrac{b}{\overline{ca}}\)
Cho tỉ lệ thức \(\dfrac{\overline{abc}}{a+\overline{bc}}=\dfrac{\overline{bca}}{b+\overline{ca}}\). CMR tỉ lệ thức \(\dfrac{a}{\overline{bc}}=\dfrac{b}{\overline{ca}}\)
Cho \(\dfrac{a+\overline{bc}}{\overline{abc}}=\dfrac{b+\overline{ca}}{\overline{bca}}=\dfrac{c+\overline{ab}}{\overline{cab}}\). Chứng minh rằng \(\dfrac{\overline{ab}}{c}=\dfrac{\overline{ca}}{b}=\dfrac{\overline{bc}}{a}\)
cho \(\dfrac{\overline{abc}}{\overline{bc}}=\dfrac{\overline{bca}}{\overline{ca}}=\dfrac{\overline{cab}}{\overline{ab}}\). Tính \(\dfrac{a}{\overline{bc}}+\dfrac{b}{\overline{ca}}+\dfrac{c}{\overline{ab}}\)
Cho \(\dfrac{\overline{abc}}{a+\overline{bc}}=\dfrac{\overline{bca}}{b+\overline{ca}}\). Chứng minh: \(\dfrac{a}{\overline{bc}}=\dfrac{b}{\overline{ca}}\)
Cho:\(\dfrac{a+\overline{bc}}{\overline{abc}}=\dfrac{b+\overline{ca}}{\overline{bca}}=\dfrac{c+\overline{ab}}{\overline{cab}}\)
CMR:\(\overline{\dfrac{bc}{a}=\dfrac{\overline{ca}}{b}=\dfrac{\overline{ab}}{c}}\)
Cho biết \(\dfrac{\overline{abc}}{\overline{bc}}=\dfrac{\overline{bca}}{\overline{ca}}=\dfrac{\overline{cab}}{\overline{ab}}\)
Tính tổng\(\dfrac{a}{\overline{bc}}+\dfrac{b}{\overline{ca}}+\dfrac{c}{\overline{ab}}\)
Cho tỉ lệ thức \(\overline{\dfrac{abc}{a+\overline{bc}}}=\overline{\dfrac{bca}{b+\overline{ca}}}.\) Chứng minh tỉ lệ thức \(\dfrac{a}{\overline{bc}}=\dfrac{b}{\overline{ca}}\)
Cho \(\dfrac{\overline{ab}+\overline{bc}}{a+c}=\dfrac{\overline{bc}+\overline{ca}}{b+c}=\dfrac{\overline{ca}+\overline{ab}}{c+a}\)
CMR : a = b = c
\(k=\dfrac{\overline{ab}}{\overline{abc}}=\dfrac{\overline{bc}}{\overline{bca}}=\dfrac{\overline{ca}}{\overline{cab}}\)
Tính giá trị của k
Áp dụng tính chất cảu dãy tỉ số bằng nhau ta có:
\(k=\dfrac{\overline{ab}}{\overline{abc}}=\dfrac{\overline{bc}}{\overline{bca}}=\dfrac{\overline{ca}}{\overline{cab}}=\dfrac{\overline{ab}+\overline{bc}+\overline{ca}}{\overline{abc}+\overline{bca}+\overline{cab}}\)
\(=\dfrac{10a+b+10b+c+10c+a}{100a+10b+c+100b+10c+a+100c+10a+b}\)
\(=\dfrac{11a+11b+11c}{111a+111b+111c}=\dfrac{11.\left(a+b+c\right)}{111.\left(a+b+c\right)}=\dfrac{11}{111}\)
Vậy \(k=\dfrac{11}{111}\)
Chúc bạn học tốt!!!