Showing posts with label solving. Show all posts
Showing posts with label solving. Show all posts

Thursday, October 24, 2013

Solving Equations Quadratic in Form

In this section, we make use of all the techniques that we have learned so far for solving quadratic equations. In fact, the equations found here are reducible to quadratic form.
Here are most of the reducible equations that we are likely to encounter. Begin by trying to identify what can be squared to obtain the leading variable term.
Tip: Look at the middle term for a hint as to what u should be.
In the previous solved problem, we certainly could have distributed the expression on the left side, put the equation in standard form then re-factored it. Instead, here we are illustrating a technique that will be used to easily solve many other equations that are quadratic in form.

Solve by making a u-substitution.
 
 
 

Solve: x^6 + 26x^3 -27
 
Six Answers: { -3, 1, (3±3iSqrt(3))/2, (-1±iSqrt(3))/2 }

So far we have been able to factor after we make the u-substitution.  If the resulting quadratic equation does not factor, then use the quadratic formula.
YouTube Videos:

---

Tuesday, July 23, 2013

Solving Nonlinear Systems

In this guide, we have solved linear systems using three methods: by graphing, substitution, and elimination.  When solving nonlinear systems, we typically choose the substitution method, however, sometimes the other methods work just as well.  Remember that to solve a system of equations means to find the common points - if they exist. Given a system of equations consisting of a circle and a line then there can be three possibilities for solutions.  Remember that solutions to a system are ordered pairs (x, y). These will be the points where they intersect.
  
Solve the nonlinear systems.

 

  
Given a circle and a parabola there are five possibilities for solutions.
  
  
These nonlinear systems given algebraically might look like:
To find the points in common, we will usually use the substitution method. But, as in this case, the graphing and elimination method work just as well.

Solve.

 

 

Certainly there are many ways to solve these problems. Experiment with other methods and see if you obtain the same results.

Solve.

 

 

 

 

YouTube Videos:





---