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504 Appendix A: Functions and Instructions
8992APPA.DOC TI-89 / TI-92 Plus: Appendix A (US English) Susan Gullord Revised: 02/23/01 1:48 PM Printed: 02/23/01 2:21 PM Page 504 of 132
For the
EXACT
setting of the
Exact/Approx
mode,
portions that cannot be solved are returned as
an implicit equation or inequality.
exact(solve((x
ì
a)
e
^(x)=
ë
x
ù
(
x
ì
a
)
,x
))
¸
e
x
+
x
=
0 or x
=
a
Use the “|” operator to restrict the solution
interval and/or other variables that occur in the
equation or inequality. When you find a solution
in one interval, you can use the inequality
operators to exclude that interval from
subsequent searches.
In Radian angle mode:
solve(tan(x)=1/x,x)
|
x>0 and x<1
¸
x
=.860
...
false
is returned when no real solutions are
found.
true
is returned if
solve()
can determine
that any finite real value of
var
satisfies the
equation or inequality.
solve(x=x+1,x)
¸
false
solve(x=x,x)
¸
true
Since
solve()
always returns a Boolean result,
you can use “and,” “or,” and “not” to combine
results from
solve()
with each other or with
other Boolean expressions.
2x
ì
11 and solve(x^2ƒ9,x)
¸
x
1 and x
ƒ
ë
3
Solutions might contain a unique new
undefined variable of the form @
nj
with
j
being
an integer in the interval 1–255. Such variables
designate an arbitrary integer.
In Radian angle mode:
solve(sin(x)=0,x)
¸
x
=
@n1
ø
p
In real mode, fractional powers having odd
denominators denote only the real branch.
Otherwise, multiple branched expressions such
as fractional powers, logarithms, and inverse
trigonometric functions denote only the
principal branch. Consequently,
solve()
produces only solutions corresponding to that
one real or principal branch.
Note: See also
cSolve()
,
cZeros()
,
nSolve()
, and
zeros()
.
solve(x^(1/3)=
ë
1,x)
¸
x
=
ë
1
solve(‡(x)=
ë
2,x)
¸
false
solve(
ë
‡(x)=
ë
2,x)
¸
x
=
4
solve(
equation1
and
equation2
[
and
…
]
, {
varOrGuess1
,
varOrGuess2
[
,
…
]
})
⇒
Boolean expression
Returns candidate real solutions to the
simultaneous algebraic equations, where
each
varOrGuess
specifies a variable that you
want to solve for.
Optionally, you can specify an initial guess
for a variable. Each
varOrGuess
must have the
form:
variable
– or –
variable
=
real or non-real number
For example,
x
is valid and so is
x=3
.
solve(y=x^2
ì
2 and
x+2y=
ë
1,{x,y})
¸
x=1 and y=
ë
1
or x=
ë
3/2 and y=1/4