minhthien2016

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These are questions asked by minhthien2016

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. 

I want to find the numbers a, b, c, d, t, m, n of this equation. I tried
 

restart:
 k := 0:
 for a to 10 do
for b to 10 do 
for c to 10 do 
for d to 10 do 
for t to 2 do 
for m to 10 do
for n to 10 do 
if a > c and igcd(a, b, c, d, t, m, n) = 1 and abs(b)+abs(d)-n <> 0 then X := [solve(abs(a*x+b)+abs(c*x+d)-t*x^2+m*x-n = 0)]; if nops(X) = 6 and type(X[1], integer) and type(X[2], integer) and type(X[3], integer) and type(X[4], integer) and type(X[5], integer) and type(X[6], integer) then k := k+1; L[k] := [a, b, c, d, t, m, n, X[]] 
end if end if
end do end do end do end do end do end do end do; 
L := convert(L, list); 
k; 
L;

I can not get the result for along time. How can I get the result and reduce the time?

I am trying to find six integer numbers a, b, c, d, n, p so that this equation
abs(a*x+b)+abs(c*x+d)+x^2+n*x+p = 0
has 6 integer solutions are 1, 2, 3, 4, 5, 6. I tried
f:=x-> abs(a*x+b)+abs(c*x+d)+x^2+n*x+p;
solve([f(1) = 0, f(2) = 0, f(3) = 0, f(4) = 0, f(5) = 0, f(6) = 0], [a, b, c, d, n, p])


This equation has no solution. Is there six integer numbers a, b, c, d, n, p so that this equation has 6 integer solutions?

I have just found one solution is
solve(abs(-2*x+5)+abs(-2*x+9)-x^2+7*x-16 = 0, x);

With Mathematica, I see at here 
https://mathematica.stackexchange.com/questions/212808/find-integers-a-b-c-d-m-n-p-so-equation-has-six-distinct-solutions

Let be the sequence (an) so that a1 = 1, a(n+1) = 5*a(n) + sqrt(k*a(n)^2 -8), for all n >=1. I know that, the answer is k = 24.  How can I choice number k so that the sequence is an integer sequence?

I want to find coodinates of the point A, B, C, D and X of a problem 6 at IMO 2018 https://www.imo-official.org/problems.aspx

I tried 

 

restart:
 with(Student:-MultivariateCalculus):
 A := [0, 0]; 
B := [5, 0]; 
C := [3, 4]; 
DD := [a, 2]; 
solve([Distance(B, A)*Distance(C, DD) = Distance(B, C)*Distance(A, DD)], [a]);

How can I get coordinate X lies inside life request?

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