 | ■No23251に返信(ゆちさんの記事)
> a+b+c=6, ab+bc+ca=11, abc=6のとき、
> a/bc+b/ca+c/abの値を求めよ。
In[1]:=
f1 = a + b + c - 6;
f2 = a*b + b*c + c*a - 11;
f3 = a*b*c - 6;
f = a/(b*c) + b/(c*a) + c/(a*b) - k;
In[5]:=
GB = GroebnerBasis[{f1, f2, f3, f},
{x, y, k}]
Out[5]=
{6 - 11*a + 6*a^2 - a^3, -11 + 6*a - a^2 +
6*c - a*c - c^2, -6 + a + b + c,
6*a - a^2 - 6/c - a*c, 6/b - a*c,
-11 + 6/a + 6*a - a^2, -7 + 3*k}
In[6]:=
Solve[% == {0, 0, 0, 0, 0, 0, 0},
{a, b, c, k}]
Out[6]=
{{k -> 7/3, b -> 1, c -> 2, a -> 3},
{k -> 7/3, b -> 1, c -> 3, a -> 2},
{k -> 7/3, b -> 2, c -> 1, a -> 3},
{k -> 7/3, b -> 2, c -> 3, a -> 1},
{k -> 7/3, b -> 3, c -> 1, a -> 2},
{k -> 7/3, b -> 3, c -> 2, a -> 1}}
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