## 345 Reputation

7 years, 160 days

## How many roots are there in this equatio...

Maple

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?

## Another way to find the length of edges ...

Maple

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:
ListTools[Categorize];
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;
nops(L);
L;

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

## How do I find the maximize and minimize ...

Maple

I want to find the maximize and minimize of the function
f:=x->(cos(x)+sqrt(3)*sin(x))/(cos(x)+sin(x)+2);
I tried
minimize(f(x), x, location = 'true');
and
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 are length s...

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

## How can I select four vertices of a list...

Maple

I have a list L:=[[0,0,0], [1,0,0], [1,1,0], [0,1,0], [0,0,1], [1,0,1], [1,1,1], [0,1,1]] (8 vertices of a cube). How can I select four vertices of the list to make a regular tetrahedron?

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