1 | initial version |

We do not know what is `sol`

, but i suppose it is the following...

```
sage: var('r');
sage: eq = 3*(2.2 + (64/r)^(1/3)) == 4*(2.2 + (128/(r-1))^(1/4))
sage: sol = solve(eq, r)
sage: sol
[r^(1/3) == 60*(r - 1)^(1/4)/(40*8^(1/4) + 11*(r - 1)^(1/4))]
```

It is clear that we cannot ask for the numerical value of `sol[0]`

.

Instead, we could help sage deliver the needed value. We just substitute $$ r = R^3 $$ and rewrite the given equation in the form: $$

\left(\frac {128}{R^3-1}\right)^{1/4}\ . $$ Rising both sides to the fourth power leads to a polynomial equation, which we can solve. We obtain one value of $R$, introduced by taking the fourth power. But it leads to no solution in $r$.

Try a plot of the difference to see there is no solution.

If there is some typo, then fix it, find an interval where the difference function changes the sign, then use `gp`

-solve. (Inside pari or inside sage.)

2 | No.2 Revision |

We do not know what is `sol`

, but i suppose it is the following...

```
sage: var('r');
sage: eq = 3*(2.2 + (64/r)^(1/3)) == 4*(2.2 + (128/(r-1))^(1/4))
sage: sol = solve(eq, r)
sage: sol
[r^(1/3) == 60*(r - 1)^(1/4)/(40*8^(1/4) + 11*(r - 1)^(1/4))]
```

It is clear that we cannot ask for the numerical value of `sol[0]`

.

Instead, we could help sage deliver the needed value. We just substitute
$$
r = R^3
$$
and rewrite the given equation in the form:
~~$$~~

{22}{10} = \left(\frac {128}{R^3-1}\right)^{1/4}\ . $$ Rising both sides to the fourth power leads to a polynomial equation, which we can solve. We obtain one value of $R$, introduced by taking the fourth power. But it leads to no solution in $r$.

Try a plot of the difference to see there is no solution.

If there is some typo, then fix it, find an interval where the difference function changes the sign, then use `gp`

-solve. (Inside pari or inside ~~sage.) ~~

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