minhthien2016

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7 years, 188 days

MaplePrimes Activity


These are questions asked by minhthien2016

I am trying to solve this equation, I tried
 

restart; 
ListTools[Categorize]; 
L := []; 
for a to 20 do
 for b to 20 do 
for c to 20 do 
for d to 20 do 
for e to 20 do 
for f to 20 do 
for g to 20 do 
for h to 20 do 
if sqrt(a+b*sqrt(c+d*sqrt(e +f*sqrt(g)))) = h then L := [op(L), [a, b, c, d, e, f, g, h]] end if
 end do end do end do end do end do end do end do end do; nops(L)

where g is not a square of a integer number . I do not get any solutions for a long time. How to reduce timing to solve this equation?

 

I know that, tetrahedron with vertices (0, 0, 0), (3, 0, 0), (0, 5, 0), (0, 0, 14) has center of insphere is  (1, 1, 1) and radius R = 1. How to create a tetrahedron whose coordinates of all vertices are integers, the inscribed spherical center and the inscribed spherical radius are integers?

This  is a question from https://mathematica.stackexchange.com/questions/239055/how-to-reduce-the-time-to-solve-this-system-of-equations. How to reduce the time in Maple?
 

  {x, y, z, a, b, m, n} /. Solve[{1/x + 1/y == 1/z, a/x  + b/y == m/n, 2 <= x <= 30, 2 <= y <= 30, 1 <= z <= 30, 2 <= a <= 10, 2 <= b <= 10, a > b, 2 <= m <= 10, 2 <= n <= 10, x > y, GCD[m, n] == 1, GCD[a, b, m] == 1, m <= n}, {x, y, z, a, b, m, n}, Integers]

I am trying to find one option so that  a sphere is tangent with every edge of a tetrahedron. Suppose tetrahedron OABC, here O(0,0,0), A(x1, y1, z1), B(x2, y2, z2), and C(x3, y3, z3).  How to find a sphere is tangent with every edge of a tetrahedron?

I am trying to  find the funtion of this graph 

I tried
f := x -> a12*x^12 + a1*x^11 + a2*x^10 + a3*x^9 + a4*x^8 + a5*x^7 + a6*x^6 + a7*x^5 + a8*x^4 + a9*x^3 + a10*x^2 + a11*x + a13;
solve([f(-4) = 3, f(-3) = 1, f(-2) = 1, f(-1) = 1, f(0) = 0, f(1) = -1, f(3) = -5, f(4) = -5, f(5) = 1, eval(diff(f(x), x), x = -2.5) = 0, eval(diff(f(x), x), x = -1.5) = 0, eval(diff(f(x), x), x = 3.5) = 0, f(6) = 3], [a12, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a13]);

I got

[[a12 = 4.697405911*10^(-6), a1 = -0.00006250181861, a2 = -1.444112429*10^(-6), a3 = 0.002660698702, a4 = -0.004689494622, a5 = -0.04291772722, a6 = 0.08407481146, a7 = 0.3251529098, a8 = -0.4752692626, a9 = -1.066462933, a10 = 0.3958806924, a11 = -0.2183704462, a13 = 0.]]

plot(4.697405911*10^(-6)*x^12 - 0.00006250181861*x^11 - 1.444112429*10^(-6)*x^10 + 0.002660698702*x^9 - 0.004689494622*x^8 - 0.04291772722*x^7 + 0.08407481146*x^6 + 0.3251529098*x^5 - 0.4752692626*x^4 - 1.066462933*x^3 + 0.3958806924*x^2 - 0.2183704462*x, x = -4 .. 5)

It doesn't like the graph of the first picture. 

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