solving radical equations and inequalities algebra ii january 24 & 25
Post on 15-Jan-2016
219 Views
Preview:
TRANSCRIPT
Solving Radical Equations and Inequalities
Algebra IIJanuary 24 & 25
Warm - Up
53
323
2
64
Evaluate the following expressions.
1. 2.
Solution: 16 Solution: - 8
Radicals/ExponentsWhat does it mean when you have a
fractions as an exponent? Such as:
4
3x
What this stands for is: the number in the numerator is the power, and the number in the denominator is the radical power.
So I could write this in another way like:
43 x mnmnn
m
aaa )()(1
Write each statement in a different form than given.1.
2.
3.
5
4x
35 x
5x
1.
2.
3.
54 x
3
5x
5
2xmnmnn
m
aaa )()(1
What about negative exponents?Remember negative exponent means your doing the inverse.
2
5x
2
5
1
x
25
1
x
Write each statement in a different form than given.1.
2.
3.
5
4x
4
38
1
5x
1.
2.
3.
54
1
x1
16
5
5
1 x
xx
Rational Exponents Solve the following rational exponential
equation:
4 3x
1
4 3x Step 1: Convert from exponent to radical form:
Step 2: eliminate the radical:
4 44( ) (3)x
Step 3: Simplify: 81x
OPTION #1
Rational Exponents
Solve the following rational exponential equation:
41 414 1(3)x
1
4 3x Step 1: Raise to the reciprocal power of the original power:
Step 2: Simplify: 81x
OPTION #2
Solving Radical EquationsA radical equation is an equation with one or more radicals that have variables in their radicand.
Solving Radical Equations Steps
Step 1 Isolate the radical on one side of the equation if necessary.
Step 2 Raise each side of the equation to the same power to get rid of the
radical.
Step 3 Solve the equation and check your solution.
Solve a radical Equation
Solve 3723 x
Write original equation.
3723 x
Cube each side. 333 372 x
Simplify. 2772 x
Subtract 7 from each side. 202 x
Divide each side by 2. x = 10
Check. Solution x = 10
Try These…
1.
2.
3.
193 x
425 x
432 3 x
SOLUTION: x = 512
SOLUTION: x = -9
SOLUTION: x = 11
Rational Exponent ExampleWhat is the solution of the equation 483 3
2
x
Write original equation.
483 3
2
x
Divide each side by 3. 163
2
x
Raise each side to the power of 3/2.
2
32
3
3
2
16
x
Simplify. x = 64
Check. Solution x = 64
Solve an equation with a rational Exponent. Solve 712 4
3
x
Write original equation.
712 4
3
x
Add 1 to each side. 82 4
3
x
Raise each side to the power of 4/3.
3
43
4
4
3
82
x
Apply exponent properties. 162x
Solve the equation. x = 14
Solution x = 14 Check.
Try These…
1.
2.
3.
3753 2
3
x
323 2
5
x
732 3
2
x
SOLUTION: x = 25
SOLUTION: x = 1
SOLUTION: x = 6
Solve an equation w/ an extraneous
solution Solve 1571 xx
Write original equation.
Square each side. 22 1571 xx
FOIL the left side and simplify the right.
Write in standard form. 01452 xx
Factor.
1571 xx
157122 xxx
027 xx
Solve. x = 7 or x = -2
Check. x = 7 (The -2 is extraneous)
Solve an equation with 2 radicalsSolve xx 312
Write original equation.
Square each side. 22312 xx
FOIL the left side and simplify the right.
Isolate the radical. xx 222 Divide both sides by 2 .
xxx 31222
xx 2Square each side again.
x = 2 or x = -1
Simplify.
xx 312
METHOD 1
222 xx
22 xx Write in standard form and factor.
0)1)(2( xx
Solve.
Check. x = -1 (The 2 is extraneous)
Solve an equation with 2 radicalsSolve xx 312
Write original equation.
xx 312
METHOD 2
Graph y1 =
12 x
Graph y2 =
x3Find the point of intersection!
You will find that the ONLY point of intersection is (-1, 2). Therefore, -1 is the only solution of the equation.
Try These… Solve the equation. Check for extraneous
solutions. 1.
2.
3.
xx4
1
2
1
3910 xx
226 xx
SOLUTION: x = 1
SOLUTION: x = 0, 4
SOLUTION: x = 3
Solve radical inequalities
5 xy
35 x
Use a graph to solve
SOLUTION
Step 1
ENTER the function and y = 3 into the graphing calculator.
GRAPH the functions from Step 1. Step 2
Step 3
Identify the x-values for which the graph of lies above the graph of y = 3.
35 x
SOLUTION: x > 14
Solve the following radical inequalities (try by hand)
1.
2.
64 x
352 x
SOLUTION: x > 32
SOLUTION: x ≥ 16
Class Work
p. 447 #3-23 oddp. 456 #5, 7, 13, 17, 23, 27, 37, 45
top related