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These are questions asked by minhthien2016

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?

I want to find the maximize and minimize of the function
I tried 
minimize(f(x), x, location = 'true');
maximize(f(x), x, location = 'true');
But I didn't get the results.  How do I find the maximize and minimize of above funciton?

How can I check six numbers: a, b, c, d, e, f are length six sides of a tetrahedron?

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