Solve

Solving equations

With the solve command, TI-Nspire CAS solves equations symbolically or numerically. Note the use of the | operator.

Logical operators

Logical operators (and, or, not, xor, nor, nand, ⇒, ⇔) are used to work with conditions and logical statements. Parentheses are important because they determine the order in which conditions are evaluated. The same notation can be used, for example, to simplify solution sets of inequalities.

Solving systems of equations

The guided tool for solving systems of equations is found under 3: Algebra > 7: Solve System of Equations.

You can add more equations later using SHIFT ENTER on a computer keyboard, or with the key on the calculator. The system template can also be typed manually: system(eq1, eq2).

Finding the location of a function’s minimum and maximum

With the commands fMin and fMax, you can determine the location of a function’s minimum and maximum values. Extrema can be studied more comprehensively using the derivative. With the solve command, the zeros of the derivative function can be determined easily.

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Solving an Equation in Physics

In physics problems, the solve command can be used to determine the unknown variable. The equation can be solved in general form or the given values can be substituted directly. If the same numerical values must be substituted in several places, this can be done using the | notation at the end of the expression. Note that TI-Nspire does not distinguish between uppercase and lowercase letters as different variables in calculations.

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Circle and sphere with CAS

You can calculate the area of a circle or the volume of a sphere using definite integrals. The solve command is used to isolate y from the equation of a circle.

Area between curves using integrals

The area between curves can be calculated by integrating the absolute value of the difference between the functions. Integrals involving absolute values may lead to difficult calculations, so an exact result is not always obtained directly. The problem can then be divided into parts by determining the order of the functions.

Vector perpendicularity and parallelism

Vector problems can be solved by combining the solve command with vector commands. The image shows examples of perpendicular, parallel, and same-direction vectors.

Three points on the same line

Whether three points lie on the same line can be examined using vectors. If vectors AB and AC are parallel, the points lie on the same line. Parallelism can be checked using the solve command or alternatively using the cross product.

Distance from a point to a line

The well-known formula for the distance from a point to a line can be derived using the Pythagorean Theorem and finding the shortest distance.

Equations related to the normal distribution

The guided normCdf command, found in the menu 5: Probability > 5: Distributions > 2: Normal Cdf..., allows you to calculate probabilities. Combined with solve, you can find missing values such as upper bound, mean, or standard deviation. Some equations require an initial guess to find a solution. Alternatively, you can use the density function and an integral.

Solving trigonometric equations

Solving trigonometric equations can be done in the CAS environment using the solve() command. Solutions can be expressed in a general form using an integer parameter or restricted to a specific interval by adding a condition. If needed, the solutions can also be converted into a list for further processing.

Solving logarithmic and exponential equations

Use the solve command to solve logarithmic and exponential equations. To define the base of the logarithm, append logbase().

Diophantine equation

There is no dedicated command for solving a Diophantine equation, but the integer n1 can be used to construct and verify a solution. The integer constant can be entered from the keyboard as @n1, where 1 is an index used to distinguish multiple integer constants.