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If an equation does not allow certain values for the unknown, guesses can
prevent these values from occurring. For example,
results in an error if x ≤ 0 (messages or ).
In the following example, the equation has more than one root, but guesses help
find the desired root.
Example:
Using Guesses to Find a Root.
Using a rectangular piece of sheet metal 40 cm by 80 cm, form an open–top box
having a volume of 7500 cm
amount to be folded up along each of the four sides) that gives the specified
volume. A taller box is preferred to a shorter one.
H
40 _ 2 H
40
H
If H is the height, then the length of the box is (80 – 2H) and the width is (40 – 2H).
The volume V is:
which you can simplify and enter as
7–8
Solving Equations
File name 33s-E-Manual-1008-Publication(1st).doc
Printed Date : 2003/10/8
y = t + log x
3
. You need to find the height of the box (that is, the
H
V = ( 80 – 2H ) × (40 – 2H ) × H
V= ( 40 – H ) × ( 20 – H ) × 4 × H
Size : 13.7 x 21.2 cm
80 _ 2 H
80
Page : 386
H
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