a,Cho abc = 27. Tính B = 3a/(ab+3a+9) + 3b/(bc+3b+9) + 3c/(ca+3c+9) b,
Cho abc = 2000. Tính C = 2000a/(ab+2000a+2000) + b/(bc+b+2000) + c/(ac+c+1)
a,Cho abc = 27. Tính B = 3a/(ab+3a+9) + 3b/(bc+3b+9) + 3c/(ca+3c+9) b,
Cho abc = 2000. Tính C = 2000a/(ab+2000a+2000) + b/(bc+b+2000) + c/(ac+c+1)
Giải thích các bước giải:
Ta có:
a,
\(\begin{array}{l}
B = \frac{{3a}}{{ab + 3a + 9}} + \frac{{3b}}{{bc + 3b + 9}} + \frac{{3c}}{{ca + 3c + 9}}\\
= \frac{{3a}}{{ab + 3a + 9}} + \frac{{3ab}}{{abc + 3ab + 9a}} + \frac{{3abc}}{{{a^2}bc + 3abc + 9ab}}\\
= \frac{{3a}}{{ab + 3a + 9}} + \frac{{3ab}}{{27 + 3ab + 9a}} + \frac{{3.27}}{{27a + 3.27 + 9ab}}\\
= \frac{{3a}}{{ab + 3a + 9}} + \frac{{ab}}{{9 + ab + 3a}} + \frac{9}{{3a + 9 + ab}}\\
= \frac{{3a + ab + 9}}{{ab + 3a + 9}} = 1
\end{array}\)
b,
\(\begin{array}{l}
C = \frac{{2000a}}{{ab + 2000a + 2000}} + \frac{b}{{bc + b + 2000}} + \frac{c}{{ca + c + 1}}\\
= \frac{{2000a}}{{ab + 2000a + 2000}} + \frac{{ab}}{{abc + ab + 2000a}} + \frac{{abc}}{{{a^2}bc + abc + ab}}\\
= \frac{{2000a}}{{ab + 2000a + 2000}} + \frac{{ab}}{{2000 + ab + 2000a}} + \frac{{2000}}{{2000a + 2000 + ab}}\\
= \frac{{2000a + ab + 2000}}{{ab + 2000a + 2000}} = 1
\end{array}\)