.
Let 
.
Let 
.
Let 
.
such that 
and 
share a common complex root?
![\[17! = 355687ab8096000\]](http://latex.artofproblemsolving.com/a/6/d/a6d147d3866c4f1fe6dac9481e53d1354891388b.png)
for some digits 
and 
.
that is missing above.
be the polynomial with leading coefficent 1 and rational coefficents, such that ![\[p\left(\sqrt{3 + \sqrt{3 + \sqrt{3 + \ldots}}}\right) = 0,\]](http://latex.artofproblemsolving.com/0/f/4/0f472be9f2cede0221e1b4d970d65de94dba01b9.png)
and with the least degree among all such polynomials. Find 
.
Y by
The sides of triangle are 
, 
and 
for some positive rational . Angle of triangle is 
degree. Find perimeter
, 
and 
for some positive rational . Angle of triangle is 
degree. Find perimeterThis post has been edited 1 time. Last edited by lneis1, Jan 30, 2021, 10:53 AM
.
which means the perimeter is 
it cancels out with the 
and gives:
This gives 
so 
.
