Computer chips, algebra homework help

Refer to the information on

page 422

to describe how the cost and the number of units manufactured are related. Rewrite the manufacturing equation C = 10n2/3 + 1500 as a radical equation, and write a step by ­step explanation of how to determine the maximum number of chips the company could make for $10,000.

7-7
Solving Radical Equations
and Inequalities
Main Ideas
Solve equations
containing radicals
• Solve inequalities
containing radicals
GET READY for the Lesson
Computer chips are made from the element silicon, which is found in
sand. Suppose a company that manufactures computer chips uses the
formula C = 10n3 + 1500 to estimate the cost in dollars of
producing n chips. This can be rewritten as a radical equation.
New Vocabulary
radical equation
extraneous solution
radical inequality
Solve Radical Equations Equations with radicals that have variables
the radicands are called radical equations. To solve this type of equation,
raise each side of the equation to a power equal to the index of the
radical to eliminate the radical.
It is very important that you check your solution. Sometimes you will
obtain a number that does not satisfy the original equation. Such a
number is called an extraneous solution.
EXAMPLESolve Radical Equations
Solve each equation.
a. Vx+1 +2 = 4
Vx+1 +2 = 4 Original equation
Vx + 1 = 2 Subtract 2 from each side to isolate the radical
(7x + 1) = 22 Square each side to eliminate the radical.
Find the squares
x= 3 Subtract from each side
CHECK Vx+1 +2 = 4 Original equation
V3+1 +2 +4 Replacex with 3.
4 = 4 Simplity
1+1=4
The solution checks. The solution is 3.
b. VI – 15 = 3 – VX
VI – 15 = 3 – VX Original equation
(Vx – 15) = (3-V)2 Square each side.
x-15 = 9 – 67x + x Find the squares.
-24-6V
4= vi
42 = (V) Square each side again
16 =
Evaluate the squares
Isolate the radical
Divide each side by-6.
422 Chapter 7 Radical Equations and inequalities