Thank you very much.

Ok, i used tcoeff(T);

with(geometry):
point(A,0,4):
point(B,4,0):
Equation(line(AB,[A,B],[x,y]));

restart:

with(geometry):

point(A,9,0):

point(B,a,a):

Equation(line(AB,[A,B],[x,y]));

It is easy to see that A and B are different points, but with(geometry) can not write.

> restart:

with(geometry):

point(A,9,0):

point(B,a^2+10,7-3*a):

Equation(line(AB,[A,B],[x,y]));

line: "One of the following conditions must be satisfied " -1-a^2 <> 0 -7+3*a <> 0

I don't understand why with(geometry) can not write, although -1-a^2 <> 0 is alway true.

restart:

A:=<1,1>:

B:=<m+1,-2*m+2>: M:=<x,y>:

u:=B-A:

v:=<u[2],-u[1]>:

n:=M-A:

with(LinearAlgebra):

DotProduct(v,n,conjugate = false)=0;

How to write the equation of the line has the form a*x + b*y + c = 0? Please help me. Thank you.

This is my code

restart:

A:=<1,1>:

B:=<m+1,-2*m+2>:

u:=B-A:

v:=<u[2],-u[1]>:

v[1]* x + v[2]* y - v[1]*A[1]  - v[2]*A[2]=0;

Please comment to me. Thank you.

Your code can not write the equation of the line which passing through the two points  A(1, 1) and B(1, -2*m + 2). Please help me. 

Thank you very much.

Let O be a center of the sphere.

1) Find the equation of the plane alpha passing through the points M, N and O.

2) Find the equation of the plane beta passing through the point O and perpendicular to the line MN.

3) Let Delta be the line of intersection of the two planes alpha and beta.

3) The points for which is the point of intersection of the line Delta and the sphere S.

Note that, i repaired coordinates of the point M

This is my code

restart:

with(geom3d):

sphere(S,x^2 + y^2 + z^2 -2*x + 2*z + 1 = 0,[x,y,z]):

point(M,1, 2,1):

point(N,3, 1, -1):

point(C,coordinates(center(S))):

plane(alpha,[M,N,C],[x,y,z]):

Equation(line(MN,[M,N],t)):

a:=ParallelVector(MN):

plane(beta,[C,a],[x,y,z]): intersection(Delta,alpha,beta):

Eq:=Equation(Delta,t):

solve([x = Eq[1],y=Eq[2],z=Eq[3],Equation(S)],[x,y,z,t]);

If the point M(1, 2, -1), i don't know how get correct anserw. Please help me.

solve(sqrt(4*x + 6) - (x^3 +7*x^2 +12*x +6)^(1/3) >=x^2 - 2,x);

Thank you very much.

Thank you.

Thank you very much. I want to all possible solutions. 

Because, i want to solve the trigonometric equation

cos(x)^2 + cos(4*x) + cos(x)^4 + sin(x)^4 + cos(x)^6 + sin(x)^6 = 1/4.

If i input

simplify(expand(cos(x)^2+cos(4*x) + cos(x)^4 + sin(x)^4 + cos(x)^6 + sin(x)^6), {expand(cos(2*x))=t});

Maple did not understand. Therefore, I input

simplify(expand(cos(x)^2+cos(4*x) + cos(x)^4 + (1-cos(x)^2)^2+ cos(x)^6 + (1-cos(x)^2)^3), {expand(cos(2*x))=t});

Is there any way?