+ 2 –10 –3 –5 2 ( )( ) – 5 check using foil. -5 2 + 2 ( )( ) factor. -10 -3 if you factor...
DESCRIPTION
What inverse operation is needed to solve each of the following? addition subtraction division multiplication square root squaringTRANSCRIPT
5x3x23 2
+ 2
2x2–10 –3
–5 2
( )( )
x3 5x2x2
– 5
2 5x2
Check using FOIL.
1x 1x 1x 1x
-5- 5 2+ 2
x2
( )( )
Factor.
-10
-3
x2
5x2 2
15x9x6 2 3
If you factor out a GMF: before using the X figure, keep it, after using the X figure, discard it.
Check using FOIL.
10-3A Radical Equations
Algebra 1 Glencoe McGraw-Hill Linda Stamper
What inverse operation is needed to solve each of the following?
73x
34x
3x
103x
12x2
4x2
additionsubtractiondivision
multiplicationsquare rootsquaring
When solving radical equations you must square both sides of the equation to remove the square root sign (undo the radical symbol).
8x 22 8x Squaring is
the inverse operation of square root!
64x
When solving radical equations you must square both sides of the equation to remove the square root sign (undo the radical symbol).
8x 22 8x
64x
8x 864 88
CAUTIONCAUTION:: Squaring both sides of an equation can introduce a solution to the squared equation that does not satisfy the original equation. Such a solution is called an extraneous solution. When you solve by squaring both sides of an equation, check each solution in the original equation.
Check
Example 1 51x
Solve.Example 2 010x
Example 305x
Isolate the radical on one
side of the equal sign before you undo the radical!
Example 4 163x8
Example 5 621x3
Example 1 51x
22 51x
251x
24x
1 1
Solve.Example 2 010x
10x
22 10x
100x
10 10
Example 305x
5x
22 5x
25x
No solution
5 5
Solve.Example 4 163x8
23x 22 23x
43x
7x
8 8
3 3
Example 5 621x3
81x3
22 81x3 641x3
63x3
21x
2 2
1 1
3 3
Okay to keep fractional answers
improper, but in lowest terms!
Solve.135x2 )1
87x
22 135x2
1695x2
174x2 5 5
2 2
53x24 )2
13x2
13x2
No Solution
4 4
1 1
Solve.8105x )3
9x
33x45 )4
25x
22 25x
45x
23x4
23x4
22 23x4
43x4
7x4
47x
10 10
5 5
5 5
3 3
1 1
Solve.
395x4 )5
180x
322x3 )6
125x4
22
125x4
1445x4
45
45
22 322x3 342x3
9 9
122x3
10x3
310x
Solve.
431x8x )7 2
222 431x8x
1631x8x2
0158xx2 03x5x
05x 03x 5x 3x
153
85
27x21x2 )8 2
222 27x21x2
47x21x2 2
- 1+ 22
x2
( )( )
011x21x2 2
-22
21
x2
22
-1
11x2 11x 1x2 0
001x2011x
21,11
Solve.
52
543x5
2 )8
1039x
563x5
2
22
563x5
2
25363x5
2
2539x5
2
25
25
54
54
3 2575
1
5
9)
10-A10 Pages 544-546 #11-22,70-75.