Equations: common information
of an equation, solving). Equivalent equations.
- 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 ) = a 2 – b 2 is an identity,
because it is valid at all values of letters, contained in it.
– a literal equality, which is valid ( i.e. it becomes an identity ) only at
values of letters, contained in it. These letters are called
values, at which an equality is valid –
roots of an equation.
Procedure of finding
roots of an equation is called
To solve an equation means to find all
Substitution of each root into an equation instead of unknown converts it into a
valid numerical equality
Two or some equations are called
, if they have the
E x a m p l e : Equations 5 x – 25 = 0 and 2 x – 7 = 3 are equivalent, because
they have the same root: x = 5 .