Based on the equation at here https://www.mapleprimes.com/questions/209660-Problem-With-RealDomainsolve

I tried solve the equation (x-1)*sqrt(x^2 - 4)=0 in Real domain. My code
restart;
RealDomain:-solve((x-1)*sqrt(x^2-4) = 0, x);

I got there solutions are 1, 2, -2.  I think, If we solve the given in RealDomain, we only get two solutions -2 and 2.

My question is: How many solutions are there in the equation (x-1)*sqrt(x^2 - 4)=0 by RealDomain:-solve?

Two pictures by using Mathematica.

I am trying to find all real solutions of the system equations 
sol := solve(And(g'(x)=0,g''(x)<>0),x)   assuming real;
I tried

restart; fprime := x-> x^6-(3/2)*x^5+2*x^4+(5/2)*x^3-7*x^2+2:
f := unapply(simplify(int(fprime(x), x)), x):
g := unapply(expand(f(x^2+2*x)), x):
sol := solve(And(g'(x)=0,g''(x)<>0),x)   assuming real;
evalf(sol);

I don't get only real solutions. How can I get only real solutions?

How to get the only solution x = (1/6)*sqrt(114)*a of this equation?
restart;
with(Student:-MultivariateCalculus);
u := `<,>`(-(1/4)*a, -(1/12)*sqrt(3)*a, -x);
v := `<,>`(-(1/2)*a, (1/6)*sqrt(3)*a, (1/2)*x);
`assuming`([solve(Angle(u, v) = arccos(2*sqrt(26)*(1/13)), x)], [And(a > 0, x > 0)])

I have the sequence f(n) satify the conditions

f(n) = 4*f(n-1)-2*f(n-2), f(1) = 1, f(2) = 28.

I find the formula of f(n)

rsolve({f(1) = 1, f(2) = 28, f(n) = 4*f(n-1)-2*f(n-2)}, {f})

I got

f(n) = (-25*sqrt(2)*(1/4)-6)*(2-sqrt(2))^n+(25*sqrt(2)*(1/4)-6)*(2+sqrt(2))^n

Is there an integeral number k satisfy the equation f(n) = k^2, (k <> 0) ?

I have problem: Let  A(2,0,0), B(0,3,0), C(0,0,6) and D(1,1,1) be four points and Delta is the line passing through the point D so that sum of distances from the points A, B, C to Delta maximum. Find a direction vector of Delta.

I tried. Let v(a,b,c) where a^2 + b^2 + c^2 = 1 and my code
 

with(Student:-MultivariateCalculus):
with(Optimization):
A := [2, 0, 0]: 
B := [0, 3, 0]: 
C := [0, 0, 6]: 
DD := [1, 1, 1]: 
v := <a, b, c>: 
d := Line(DD, v): 
d1 := Distance(A, d): 
d2 := Distance(B, d): 
d3 := Distance(C, d): 
S := d1+d2+d3: 
Maximize(S, {a^2+b^2+c^2 = 1});

I didn't get the result. How to get the numbers a, b, c?