In algebra, there is the concept of two types of equality - identities and equations.Identities - these are equality, which are feasible for all values of the letters in their inbox.Equations - is also equal, but they are feasible only for certain values of their constituent letters.The letters on the conditions of the problem are usually unequal.This means that some of them can take any valid values, called coefficients (or parameters), and others - they are known unknowns - are as to be found in the solution process.As a rule, represent unknown quantities in equations letters, the latest in the Latin alphabet (xyz etc.), or the same letters, but with the index (x1, x2, etc.), and well-known factors - the first letters of thethe alphabet.
of the number of unknowns of the equation is isolated to one, two or several unknowns.Thus, all the values of the unknowns in which to solve the equation becomes an identity, are called solutions of the equations.The equation can be regarded as a foregone conclusion in the case found all his decisions or prove that it is not represented.Setting to "solve the equation" in practice is common and means that you need to find the root of the equation.
Determination : roots of the equation are those values of the unknowns of the feasible region in which to solve the equation becomes an identity.
algorithm for solving equations of absolutely all the same, and the meaning of it is that with the help of mathematical transformations this expression lead to a simpler form.
equations that have the same roots in algebra are called equivalent.
simplest example: 7x-49 = 0, the root of the equation x = 7;
x 7 = 0, like root x = 7, therefore, the equations equivalent.(In special cases equivalent to the equation can not have roots).
If the root of the equation is also the root of other, more simple equation derived from the source through transformation, the latter called a consequence of the previous equation.
If these two equations is a consequence of one another, they are considered equivalent.Yet they are called equivalent.The above example illustrates this.
decision of even the most simple equations in practice often causes difficulty.As a result, the solution can get one root of the equation, two or more, even an infinite number - it depends on the type of equations.There are those who have no roots, they are called intractable.
Examples:
1) 15x -20 = 10;x = 2.This is the only root of the equation.
2) 7x - y = 0.The equation has an infinite set of roots, since each variable can be an infinite number of values.
3) x2 = - 16. The number raised to the second degree, always gives a positive result, so it is impossible to find the root of the equation.This is one of the unsolvable equations mentioned above.
correctness of solutions is checked by substituting the found roots instead of letters, and the decision to get an example.If the identity is respected, the decision is correct.
