852 Appendix A: Functions and Instructions
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.
2xì 1c1 and solve(x^2ƒ9,x)
¸
x
c
1 and x
ƒ
ë 3
Solutions might contain a unique new undefined
variable of the form @
n
j
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
=
@n1ø 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^2ì 2 and
x+2y=ë 1,{x,y}) ¸
x=1 and y=ë 1
or x=ë 3/2 and y=1/4
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