Question

[Bé Bánh Bao]

Tìm a, b, c

    ab=1/3

     bc=1/2

     ac=3/8

Answer 1

[Nguyễn Tấn Phát]

Ta có:

\(ab.bc.ac=\frac{1}{3}.\frac{1}{2}.\frac{3}{8}=\frac{1}{16}\)

\(\Rightarrow a^2b^2c^2=\left(abc\right)^2=\left(\pm\frac{1}{4}\right)^2\)

\(\Rightarrow abc=\pm\frac{1}{4}\)

Nếu \(abc=\frac{1}{4}\text{ thì }\hept{\begin{cases}a=\frac{abc}{bc}=\frac{\frac{1}{4}}{\frac{1}{2}}=\frac{1}{2}\\b=\frac{abc}{ac}=\frac{\frac{1}{4}}{\frac{3}{8}}=\frac{2}{3}\\c=\frac{abc}{ab}=\frac{\frac{1}{4}}{\frac{1}{3}}=\frac{3}{4}\end{cases}}\)

Nếu \(abc=-\frac{1}{4}\text{ thì }\hept{\begin{cases}a=\frac{abc}{bc}=\frac{-\frac{1}{4}}{\frac{1}{2}}=-\frac{1}{2}\\b=\frac{abc}{ac}=\frac{-\frac{1}{4}}{\frac{3}{8}}=-\frac{2}{3}\\c=\frac{abc}{ab}=\frac{-\frac{1}{4}}{\frac{1}{3}}=-\frac{3}{4}\end{cases}}\)

Vậy \(\left(a;b;c\right)=\left\{\left(\frac{1}{2};\frac{2}{3};\frac{3}{4}\right);\left(\frac{-1}{2};\frac{-2}{3};\frac{-3}{4}\right)\right\}\)