1) Alg,Trig &Log Equations
1) Radical Equation
Solve sqrt(2*x+5)=sqrt(x)+sqrt(5)
> restart;
> r:=sqrt(2*x+5)=sqrt(x)+sqrt(5);
> solve(r,x);
> plot({sqrt(2*x+5),sqrt(x)+sqrt(5)},x=0..25);
2) Trig Equation
Find the solutions of x + tan(x) =0
> restart;
> f:=x+tan(x);
> fsolve(f=0,x);
Is this the only solution?
If we plot the function we have
> plot(f,x=-2*Pi..2*Pi,-2*Pi..2*Pi);
To find all solutions:
> solve(f=0,x);
A solution in the interval (4,6) will be given by
> fsolve(f=0,x,4..6);
The solution to y=0 is the same as finding the intersection of the curves y=x and y=-tan(x).
> plot ({x,-tan(x)},x=-2*Pi..2*Pi,-2*Pi..2*Pi,color=blue);
3) Log Equation
Solve ln(x)+ln(x+1)-ln(2)=0.
> restart;
> y:=ln(x)+ln(x+1)-ln(2);
> solve(y=0);
> plot(y,x=-3..3,color=red);