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((xìa)e^(x)=ëxù
(
xìa
)
,x
))
¸
ex + 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.
2xì11 and solve(x^2ƒ9,x) ¸
x 1 and x ƒ ë3
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 = @n1øp
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)=ë1,x) ¸x = ë1
solve(‡(x)=ë2,x) ¸false
solve(ë‡(x)=ë2,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^2ì2 and
x+2y=ë1,{x,y}) ¸
x=1 and y=ë1
or x=ë3/2 and y=1/4