Math 20-1 Chapter 5 Radical Expressions and Equations 5.3 Solve Radical Equations Teacher Notes.
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Transcript of Math 20-1 Chapter 5 Radical Expressions and Equations 5.3 Solve Radical Equations Teacher Notes.
![Page 1: Math 20-1 Chapter 5 Radical Expressions and Equations 5.3 Solve Radical Equations Teacher Notes.](https://reader036.fdocuments.in/reader036/viewer/2022070414/5697c0101a28abf838ccb32a/html5/thumbnails/1.jpg)
Math 20-1 Chapter 5 Radical Expressions and Equations
5.3 Solve Radical Equations
Teacher Notes
![Page 2: Math 20-1 Chapter 5 Radical Expressions and Equations 5.3 Solve Radical Equations Teacher Notes.](https://reader036.fdocuments.in/reader036/viewer/2022070414/5697c0101a28abf838ccb32a/html5/thumbnails/2.jpg)
5.3 Radical Equations• A Radical Equation must have at least one
radicand containing a variable
• The Power Rule: Keeping Equality Balanced• If we raise two equal quantities to the same power,
the results are also two equal quantities.• If x = y then x2 = y2
• Warning: These are NOT equivalent Equations!
221743 3 3 xxxxx
The values for the variable in the radicand must be considered when solving. 5.3.1
![Page 3: Math 20-1 Chapter 5 Radical Expressions and Equations 5.3 Solve Radical Equations Teacher Notes.](https://reader036.fdocuments.in/reader036/viewer/2022070414/5697c0101a28abf838ccb32a/html5/thumbnails/3.jpg)
• Start with a simple original equation:• x = 3• Square both sides to get a new equation:• x2 = 32 which simplifies to x2 = 9• The only solution to x = 3 is 3• x2 = 9 has two solutions 3 and -3• -3 is considered extraneous
Extraneous RootsAn extraneous root is a number obtained in solving an equation that does not satisfy the initial restrictions on the variable.
5.3.2
![Page 4: Math 20-1 Chapter 5 Radical Expressions and Equations 5.3 Solve Radical Equations Teacher Notes.](https://reader036.fdocuments.in/reader036/viewer/2022070414/5697c0101a28abf838ccb32a/html5/thumbnails/4.jpg)
Equations Containing One Radical
Isolate the radical term on one side of the equation and then apply the Power Rule with squares.
Determine the roots of the radical equation:
3 4x
2 2
3 4x
3 16x 13x
Verify by substitut
3 4
16 4
4
ion
13
:
4
a) 3 4x
Verify the radicand restrictions
3 0
3x
x
5.3.3
![Page 5: Math 20-1 Chapter 5 Radical Expressions and Equations 5.3 Solve Radical Equations Teacher Notes.](https://reader036.fdocuments.in/reader036/viewer/2022070414/5697c0101a28abf838ccb32a/html5/thumbnails/5.jpg)
Equations Containing One Radicalb) 2 4x x
2242 xx
28162 xxx 29140 xx
1490 2 xx)2)(7(0 xx
7, 2x
Verify by sub :
7
7 72 4
9 3
3 3
x
2 4
4 2
2
2 2
2 2
x
Therefore the solution is x = 2.
5.3.4
Why would just verifying the radicand restrictions not be sufficient in this case?
![Page 6: Math 20-1 Chapter 5 Radical Expressions and Equations 5.3 Solve Radical Equations Teacher Notes.](https://reader036.fdocuments.in/reader036/viewer/2022070414/5697c0101a28abf838ccb32a/html5/thumbnails/6.jpg)
Your TurnAlgebraically determine the roots of
Equations Containing One Radical
xx 4330
4330 xx
224330 xx
1450 2 xx
)2)(7(0 xx
7, 2x
3
V
0
erify by sub:
7
73( ) 4
9
3 3
7
3
x
30 3( 2
2
) 4
36 6
6 6
2
x
Therefore the solution is x = 7.5.3.5
Can you just verify the radicandrestrictions?
![Page 7: Math 20-1 Chapter 5 Radical Expressions and Equations 5.3 Solve Radical Equations Teacher Notes.](https://reader036.fdocuments.in/reader036/viewer/2022070414/5697c0101a28abf838ccb32a/html5/thumbnails/7.jpg)
Equations Containing Two Radicals• Separate the radicals: one on each side of the equality sign• Square both sides of the equation, not individual terms• If a radical is still present, isolate that radical and square both sides a second time
Algebraically determine the roots
a) 4 60x x
2 2
4 60x x
224 60x x
16 60x x
15 60x
4x
4 60x x
4 4 64 0
4 2 64
8 8
Verify by sub:
4x
5.3.6
Verify the radicand restrictions
![Page 8: Math 20-1 Chapter 5 Radical Expressions and Equations 5.3 Solve Radical Equations Teacher Notes.](https://reader036.fdocuments.in/reader036/viewer/2022070414/5697c0101a28abf838ccb32a/html5/thumbnails/8.jpg)
Equations Containing Two RadicalsSolve 2 3 7 2x x
2 3 7 2x x
2 3 2 7x x
2 2
2 3 2 7x x
2 2
2 3 2 7x x
2 3 4 4 7 7x x x
2 3 4 7 11x x x 14 4 7x x
2214 4 7x x
Verify the radicand restrictions.
5.3.7
![Page 9: Math 20-1 Chapter 5 Radical Expressions and Equations 5.3 Solve Radical Equations Teacher Notes.](https://reader036.fdocuments.in/reader036/viewer/2022070414/5697c0101a28abf838ccb32a/html5/thumbnails/9.jpg)
2 28 196 16( 7)x x x 2 28 196 16 112x x x
2 44 84 0x x
( 42)( 2) 0x x
42 0 or - 2 0x x or 42 2 x x
Equations Containing Two Radicals
:
42
Check
x
2( ) 3 7 2
81 49
42 4
2
9 7 2
2
2
2
:
2
Check
x
2( ) 3 7 2
1
2 2
9 2
1 3 2
2 2
Therefore x = 42
5.3.8
![Page 10: Math 20-1 Chapter 5 Radical Expressions and Equations 5.3 Solve Radical Equations Teacher Notes.](https://reader036.fdocuments.in/reader036/viewer/2022070414/5697c0101a28abf838ccb32a/html5/thumbnails/10.jpg)
Your Turn
Solve:
Equations Containing Two Radicals
2 3 2 2x x
2 3 2 2x x
2 3 2 2x x
2 2
2 3 2 2x x
2 3 4 4 2 2x x x
3 4 2x x
223 4 2x x
2 6 9 16( 2)x x x
5.3.9
![Page 11: Math 20-1 Chapter 5 Radical Expressions and Equations 5.3 Solve Radical Equations Teacher Notes.](https://reader036.fdocuments.in/reader036/viewer/2022070414/5697c0101a28abf838ccb32a/html5/thumbnails/11.jpg)
2 6 9 16 32x x x 2 22 23 0x x
( 23)( 1) 0x x or 23 1x x
Equations Containing Two Radicals
:
23
Check
x
2( ) 3 2 2
49 25
23 2
2
7 5 2
2
3
2
:
1
Check
x
2( ) 3 2 2
1
1
1
1
2
0 2
Therefore x = 23
5.3.10
![Page 12: Math 20-1 Chapter 5 Radical Expressions and Equations 5.3 Solve Radical Equations Teacher Notes.](https://reader036.fdocuments.in/reader036/viewer/2022070414/5697c0101a28abf838ccb32a/html5/thumbnails/12.jpg)
AssignmentSuggested Questions:
Page 300:2, 3a,b, 4a,b, 5, 6b, 7a, 8a,c, 9d, 10a,d12, 13, 15,
5.3.11