Casio ALGEBRA FX 2.0 Manual de usuario

19990401

Chapter

Equation Calculations

Your graphic calculator can perform the following three types of

calculations:

•Simultaneous linear equations

•High degree equations

•Solve calculations

From the Main Menu, enter the EQUA Mode.

• {SIML} ... {linear equation with 2 to 30 unknowns}

• {POLY} ... {degree 2 to 30 equations}

• {SOLV} ... {solve calculation}

4-1 Simultaneous Linear Equations

4-2 High Degree Equations

4-3 Solve Calculations

4-4 What to Do When an Error Occurs

19990401

4-1-1

Simultaneous Linear Equations

4-1 Simultaneous Linear Equations

Description

You can solve simultaneous linear equation with two to 30 unknowns.

•Simultaneous Linear Equation with Two Unknowns:

a1x1+ b1x2= c1

a2x1+ b2x2= c2

•Simultaneous Linear Equation with Three Unknowns:

a1x1+ b1x2+ c1x3= d1

a2x1+ b2x2+ c2x3= d2

a3x1+ b3x2+ c3x3= d3

Set Up

1. From the Main Menu, enter the EQUA Mode.

Execution

2. Select the SIML (simultaneous equation) Mode, and specify the number of unknowns

(variables).

You can specify from 2 to 30 unknowns. To specify more than six unknowns, press

6(n) and then input a value.

3. Sequentially input the coefficients.

The cell that is currently selected for input is highlighted. Each time you input a

coefficient the highlighting shifts in the sequence:

a1→b1→c1 →… an→bn→cn→(n= 2 to 30)

You can also input fractions, complex numbers, and values assigned to variables as

coefficients.

You can cancel the value you are inputting for the current coefficient by pressing iat

any time before you press wto store the coefficient value. This returns to the

coefficient to what it was before you input anything. You can then input another value if

you want.

To change the value of a coefficient that you already stored by pressing w, move the

cursor to the coefficient you want to edit. Next, input the value you want to change to or

press 1(EDIT).

Pressing 3(CLR) clears all coefficients to zero.

4. Solve the equations.

…

19990401

4-1-2

Simultaneous Linear Equations

○○○○○

Example To solve the following simultaneous linear equations for x, y, and z

4x+y–2z=–1

x+6y+3z= 1

– 5x+4y+z=–7

Procedure

1mEQUA

21(SIML)

2(3)

3ewbw-cw-bw

bwgwdwbw

-fwewbw-hw

46(SOLV)

Result Screen

#Internal calculations are performed using a 15-

digit mantissa, but results are displayed using

a 10-digit mantissa and a 2-digit exponent.

#Simultaneous linear equations are solved by

inverting the matrix containing the coefficients

of the equations. For example, the following

shows the solution (x1, x2, x3) of a simultane-

ous linear equation with three unknowns.

x1a1b1c1–1 d1

x2=a2b2c2d2

x3a3b3c3d3

Because of this, precision is reduced as the

value of the determinant approaches zero. Also,

simultaneous equations with three or more

unknowns may take a very long time to solve.

#An error occurs if the calculator is unable to find

a solution.

#After calculation is complete, you can press

1(REPT), change coefficient values, and then

re-calculate.

19990401

4-2-1

High Degree Equations

# Internal calculations are performed using a

15-digit mantissa, but results are displayed

using a 10-digit mantissa and a 2-digit

exponent.

#Equations of third degree or higher may take

a very long time to solve.

#An error occurs if the calculator is unable to find

a solution.

# After calculation is complete, you can press

1(REPT), change coefficient values, and then

re-calculate.

4-2 High Degree Equations

Description

You can use this calculator to solve high degree equations such as quadratic equations and

cubic equations.

•Quadratic Equation:

ax2+ bx + c= 0 (a≠0)

•Cubic Equation:

ax3+ bx2+ cx + d = 0(a≠0)

Set Up

1. From the Main Menu, enter the EQUA Mode.

Execution

2. Select the POLY (high degree equation) Mode, and specify the degree of the equation.

You can specify a degree from 2 to 30. To specify a degree greater than three, press

3(n) and then input a value.

3. Sequentially input the coefficients.

The cell that is currently selected for input is highlighted. Each time you input a

coefficient the highlighting shifts in the sequence:

a→b→c→…

You can also input fractions, complex numbers, and values assigned to variables as

coefficients.

You can cancel the value you are inputting for the current coefficient by pressing iat

any time before you press wto store the coefficient value. This returns to the

coefficient to what it was before you input anything.You can then input another value if

you want.

To change the value of a coefficient that you already stored by pressing w, move the

cursor to the coefficient you want to edit. Next, input the value you want to change to or

press 1(EDIT).

Pressing 3(CLR) clears all coefficients to zero.

4. Solve the equations.

…

19990401

4-2-2

High Degree Equations

○○○○○

Example To solve the cubic equation

x3– 2x2– x+ 2 = 0

Procedure

1mEQUA

22(POLY)

2(3)

3bw-cw-bwcw

46(SOLV)

Result Screen

(Multiple Solutions) (Complex Number Solution)

19990401

4-3-1

Solve Calculations

4-3 Solve Calculations

Description

The Solve Calculation Mode lets you determine the value of any variable in a formula,

without going through the trouble of solving the equation.

Set Up

1. From the Main Menu, enter the EQUA Mode.

Execution

2. Select the SOLV (Solve) Mode, and input the equation as it is written.

If you do not input an equals sign, the calculator assumes that the expression is to the

left of the equals sign, and there is a zero to the right. *1

3. In the table of variables that appears on the display, input values for each variable.

You can also specify values for Upper and Lower to define the upper and lower limits of

the range of solutions. *2

4. Select the variable for which you want to solve to obtain the solution.

“Lft” and “Rgt” indicate the left and right sides that are calculated using the solution.*3

*1An error occurs if you input more than one equals

sign.

*2An error occurs if the solution falls outside the

range you specify.

*3Solutions are approximated using Newton’s

method. Lft and Rgt values are displayed for

confirmation, because Newton’s method may

produce results that are the real solution.

The closer the difference between the Lft and

Rgt values is to zero, the lower degree of error

in the result.

#The message “Retry” appears on the display

when the calculator judges that convergence is

not sufficient for the displayed results.

19990401

4-3-2

Solve Calculations

○○○○○

Example An object thrown into the air at initial velocity V takes time T to reach

height H. Use the following formula to solve for initial velocity V when

H = 14 (meters), T = 2 (seconds) and gravitational acceleration is G =

9.8 (m/s2).

H = VT – 1/2 GT2

Procedure

1mEQUA

23(SOLV)

ax(H)!.(=)ac(V)a/(T)-(b/c)

a$(G)a/(T)xw

3bew(H = 14)

aw(V = 0)

cw(T = 2)

j.iw(G = 9.8)

4Press fto highlight V = 0, and then press 6(SOLV).

Result Screen

19990401

4-4 What to Do When an Error Occurs

uError during coefficient value input

Press the ikey to clear the error and return to the value that was registered for the

coefficient before you input the value that generated the error. Try inputting a new value

again.

uError during calculation

Press the ikey to clear the error and display coefficient. Try inputting values for the

coefficients again.

4-4-1

What to Do When an Error Occurs

kClearing Equation Memories

1. Enter the equation calculation mode (SIML or POLY) you want to use and

perform the function key operation required for that mode.

•In the case of the SIML Mode (1), use number keys to specify the number of

unknowns.

•In the case of the POLY Mode (2), use number keys to specify the degree of

the polynomial.

•If you pressed 3(SOLV), advance directly to step 2.

2. Press 2(DEL •A).

3. Press w(Yes) to delete the applicable equation memories or i(No) to abort

the operation without deleting anything.

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