Question

matlab求解方程的解析解，在线急等

(r^(1/3)-1)*((r-1)*(q/(2*(r-1)))^(2/3)+((1-q)/2)^(2/3))=(2*(r-1)/q)^(1/3)-(2*r/(1-q))^(1/3)，求q关于r的表达式，或者给出做（r，q）图的程序也行

Answer 1

(q，r)图形如下

Answer 2

画图简单：

ezplot('(r^(1/3)-1)*((r-1)*(q/(2*(r-1)))^(2/3)+((1-q)/2)^(2/3))=(2*(r-1)/q)^(1/3)-(2*r/(1-q))^(1/3)');

解析解没求到：
>> syms r q

>> solve((r^(1/3)-1)*((r-1)*(q/(2*(r-1)))^(2/3)+((1-q)/2)^(2/3))==(2*(r-1)/q)^(1/3)-(2*r/(1-q))^(1/3),q)

Warning: Explicit solution could not be found.
> In solve at 169
ans =
[ empty sym ]

>> solve((r^(1/3)-1)*((r-1)*(q/(2*(r-1)))^(2/3)+((1-q)/2)^(2/3))==(2*(r-1)/q)^(1/3)-(2*r/(1-q))^(1/3),r)
Warning: Explicit solution could not be found.
> In solve at 169
ans =
[ empty sym ]

确实求不到。。。。maple下的计算结果
solve((r^(1/3)-1)*((r-1)*(q/(2*(r-1)))^(2/3)+((1-q)*(1/2))^(2/3)) = ((2*(r-1))/q)^(1/3)-(2*r/(1-q))^(diff(1/3, x)), r);

/ (2/3)
| (4/3) (1/3) / q \
RootOf|-2 _Z 2 |------|
\ \_Z - 1/

(2/3) (2/3)
(1/3) (1/3) / q \ (1/3) / q \
+ 2 _Z 2 |------| + 2 2 |------| _Z
\_Z - 1/ \_Z - 1/

(2/3)
(1/3) (2/3) (1/3) / q \
- _Z (4 - 4 q) - 2 2 |------|
\_Z - 1/

(1/3) \
(2/3) (1/3) /_Z - 1\ |
+ (4 - 4 q) + 4 2 |------| - 4|
\ q / /
粘过来变乱码了。。。。确实没求到。。。