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These are questions asked by toandhsp

How to subs t = cos(2*x) in expression A:= cos(x)^2 + cos(4*x)? Please help me. Thank you.

I have a function 

f:=x->(x^2 + 2*m*x + m + 1)/(x -1);
Now I want to define a function as simplify(diff(f(x),x)), i did 
g:=x->simplify(diff(f(x),x)). Then, i could not calculate g(3). Please help me. Thank you.

Please write a code for the prolem:

Find the all values of paramater m for which the equation

(x-2)*(x^2 - 2*m*x + 5*m - 6) = 0 (x is unknown)

has three diffenrent real solutions.

Please write for me another code for the following problem:
Write the equation of the plane (P) passing through the line (d): x = -t -1, y = t + 3, z = 2*t + 2, (P) cuts the axis Ox at A and the axis Oy at B (A, B different form origin O) so that OA = 2OB.

This is my code






I used the command minimize such

minimize(3*x^2+2*m*x+2*m^2-3*m-6,1 <= x)

But it can not. How can i find the least of the function g:=x>3*x^2+2*m*x+2*m^2-3*m-6,  here x >=1.

Please help me. Thank you.

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