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);