# Untitled

By: a guest on Jun 17th, 2012  |  syntax: None  |  size: 1.70 KB  |  hits: 11  |  expires: Never
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1. Symbolical mathematical problem (mathematica)
2. 3/y^4==3/x^4+a/(x+2y)^4
3.
4. ans:
5.     3/(r^4 x^4) == 3/x^4 + a/(x + 2 r x)^4
6.
7. ans: Graph and 4 solutions and no its doesn't depend on `a`.
8.
9. In[538]:= eq =
10.  Eliminate[3/y^4 == 3/x^4 + a/(x + 2 y)^4 && r == y/x, {x, y}]
11.
12. Out[538]= -24 r - 72 r^2 - 96 r^3 + (-45 + a) r^4 + 24 r^5 + 72 r^6 +
13.   96 r^7 + 48 r^8 == 3
14.
15. In[539]:= r /. Solve[eq && -1 < a < 1, r, Reals]
16.
17. Out[539]= {ConditionalExpression[
18.   Root[-3 - 24 #1 - 72 #1^2 - 96 #1^3 + (-45 + a) #1^4 + 24 #1^5 +
19.      72 #1^6 + 96 #1^7 + 48 #1^8 &, 1], -1 < a < 0 ||
20.    0 < a < Root[-184528125 + 267553125 #1 + 11238750 #1^2 +
21.        110250 #1^3 - 225 #1^4 + #1^5 &, 1] ||
22.    Root[-184528125 + 267553125 #1 + 11238750 #1^2 + 110250 #1^3 -
23.        225 #1^4 + #1^5 &, 1] < a < 1],
24.  ConditionalExpression[
25.   Root[-3 - 24 #1 - 72 #1^2 - 96 #1^3 + (-45 + a) #1^4 + 24 #1^5 +
26.      72 #1^6 + 96 #1^7 + 48 #1^8 &, 2], -1 < a < 0 ||
27.    0 < a < Root[-184528125 + 267553125 #1 + 11238750 #1^2 +
28.        110250 #1^3 - 225 #1^4 + #1^5 &, 1] ||
29.    Root[-184528125 + 267553125 #1 + 11238750 #1^2 + 110250 #1^3 -
30.        225 #1^4 + #1^5 &, 1] < a < 1],
31.  ConditionalExpression[
32.   Root[-3 - 24 #1 - 72 #1^2 - 96 #1^3 + (-45 + a) #1^4 + 24 #1^5 +
33.      72 #1^6 + 96 #1^7 + 48 #1^8 &, 3],
34.   0 < a < Root[-184528125 + 267553125 #1 + 11238750 #1^2 +
35.       110250 #1^3 - 225 #1^4 + #1^5 &, 1]],
36.  ConditionalExpression[
37.   Root[-3 - 24 #1 - 72 #1^2 - 96 #1^3 + (-45 + a) #1^4 + 24 #1^5 +
38.      72 #1^6 + 96 #1^7 + 48 #1^8 &, 4],
39.   0 < a < Root[-184528125 + 267553125 #1 + 11238750 #1^2 +
40.       110250 #1^3 - 225 #1^4 + #1^5 &, 1]]}
41.