Equations: common information
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 .
