Home
Math symbols
Jokes
Forum
About us
Links
Contact us
Site map
Search The Site
   
   Program of Lessons
 
 Study Guide
 Topics of problems
 Tests & exams
www.bymath.com Study Guide - Arithmetic Study Guide - Algebra Study Guide - Geometry Study Guide - Trigonometry Study Guide - Functions & Graphs Study Guide - Principles of Analysis Study Guide - Sets Study Guide - Probability Study Guide - Analytic Geometry Select topic of problems Select test & exam Rules Price-list Registration

Equations: common information

Equality. Identity. Equation (unknowns, roots
of an equation, solving). Equivalent equations.


Equality - two expressions (numerical or literal ones), jointed by sign " = ".
Identity - a valid numerical equality or a literal equality, valid at any numerical values of letters, contained in it.

E x a m p l e s :   1)  A numerical equality  4 7 + 2 = 30 is an identity.

                           2)  A literal equality  ( a + b )( a b ) = a2 b2 is an identity,
                                because it is valid at all values of letters, contained in it.

Equation a literal equality, which is valid ( i.e. it becomes an identity ) only at some values of letters, contained in it. These letters are called unknowns and the values, at which an equality is valid roots of an equation. Procedure of finding all roots of an equation is called solving. To solve an equation means to find all its roots. Substitution of each root into an equation instead of unknown converts it into a valid numerical equality (identity). Two or some equations are called equivalent equations, if they have the same roots.

E x a m p l e :   Equations  5x 25 = 0  and  2x 7 = 3  are equivalent, because
                        they have the same root:  x = 5 .

Back


| Home | About us | Links | Contact us |

Copyright 2002-2007 Dr. Yury Berengard.  All rights reserved.