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MaplePrimes Activity

These are questions asked by minhthien2016

I want to find general formulas of the sequence satifies:
f(1) = 1, f(n+1) = 1/2*(f(n)+9/f(n))
I tried 
rsolve({f(1) = 1, f(n+1) = 1/2*(f(n)+9/f(n))}, {f})

I got the answer

How to get the form (-3*2^(2^(-1+n))+3*(-1)^(1+2^(-1+n)))/(-2^(2^(-1+n))+1)?

I am trying to find the positive integer numbers a, b, c, d, e, f so that the function y =  (a x^2 + b x + c)/(d x^2 + e x + f) is increasing function and the equation  (a x^2 + b x + c)/(d x^2 + e x + f) = x has three integer solutions. I tried
L := [];
for a to 10 do
for b to 10 do
for c to 10 do
for d to 10 do
for e to 10 do
for f to 10 do
if a*e-b*d > 0 and a^2*f^2-a*b*e*f-2*a*c*d*f+a*c*e^2+b^2*d*f-b*c*d*e+c^2*d^2 < 0 and igcd(a, b, c) = 1 and igcd(d, e, f) = 1 and igcd(a, b, c, d, e, f) = 1 and x = (a*x^2+b*x+c)/(d*x^2+e*x+f) then L := [op(L), [a, b, c, d, e, f, x]]

L:=[op(L), [a, b, c, d,e,f,x]]; fi; 
od: od: od: od:od:od: 

I did not get the result. 
With Mathematica, I got like this picture (a, b, c, d, e, f, x1, x2, x3)

How can I get the correct results?

I am trying to find formula of the sequence f(n)

f(n+1) = (1+f(n))/(2*f(n)), f(1) = -7/13

I tried
rsolve({f(1) = -7/13, f(n+1) = (1+f(n))/(2*f(n))}, {f})

But I couldn't get the result. With Mathematica, I got the result.

I want to find all complex numbers such that 
abs(z)*(z-4-I)+2*I = (5-I)*z.
I tried solve(abs(z)*(z-4-I)+2*I = (5-I)*z, z)
and got the answer is z = -1.
This is a question in a test with multiple choice. The key of question is three numbers.

Is my commant wrong? Where is wrong?

Let be given tetrahedron ABCD, where AB = BC = AC = a, AD = d, AD = e, CD = f. I know that, If the measure of angle of AB and CD equal to Pi/3, then we have d^2 - e^2 - a*f = 0. I tried:
L := []; 
for a to 30 do for d to 30 do
for e to 30 do for f to 30 do
if abs(d-e) < a and a < d+e and abs(a-e) < d and d < a+e and abs(d-a) < e and e < d+a and abs(d-f) < a and a < d+f and abs(a-f) < d and d < a+f and abs(d-a) < f and f < d+a and abs(e-f) < a and a < e+f and abs(a-f) < e and e < a+f and abs(a-e) < a and a < a+e and -a*f+d^2-e^2 = 0 and igcd(a, d, e, f) = 1 and nops({a, d, e, f}) = 4
then L := [op(L), [a, d, e, f]] end if end do end do end do end do; 

Another way to find the length of edges of a tetrahedron knowing that the mesure angle of two opposite?

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