I have the following problem: I need to solve the equation: $$\frac{\cos\left(x\right)}{x^6} - \frac{6 \sin\left(x\right)}{x^7}==0$$
and I don't really remember how to do it symbolically.
Some help would be appreciated, thanks in advance.
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Sign up to join this communityI have the following problem: I need to solve the equation: $$\frac{\cos\left(x\right)}{x^6} - \frac{6 \sin\left(x\right)}{x^7}==0$$
and I don't really remember how to do it symbolically.
Some help would be appreciated, thanks in advance.
Try this possibility
NSolve[Cos[x]/x^6 - 6 Sin[x]/x^7 == 0 && 10 < x < 30, x]
{{x -> 10.4754}, {x -> 13.725}, {x -> 16.9383}, {x -> 20.1307}, {x ->
23.31}, {x -> 26.4807}, {x -> 29.6454}}
All the x values indicates that x = 6 Tan[x] which can be deduced from your original equation.
If you use
Solve[Cos[x]/x^6 - 6 Sin[x]/x^7 == 0 && 10 < x < 30, x, Reals]
instead, you get
{{x -> Root[{-6 Sin[#1] + Cos[#1] #1 &,
10.4754178939933717338}]},
{x ->
Root[{-6 Sin[#1] + Cos[#1] #1 &, 13.7250443836508641500}]},
{x ->
Root[{-6 Sin[#1] + Cos[#1] #1 &, 16.9383246741988750253}]},
{x ->
Root[{-6 Sin[#1] + Cos[#1] #1 &, 20.1306831271422053797}]},
{x ->
Root[{-6 Sin[#1] + Cos[#1] #1 &, 23.3100136506053351414}]},
{x ->
Root[{-6 Sin[#1] + Cos[#1] #1 &, 26.4807198099258826794}]},
{x ->
Root[{-6 Sin[#1] + Cos[#1] #1 &, 29.6454356789935628843}]}}
And for all these x values, the root occurs at 6 Tan[x]