1. y = (x + 1)1/2 – 2 Algebra II
2. y = 3√ x – 2 1
Solving Radical
Equations
Algebra II
Algebra II
3
¡ Undo
what's been done
¡ Always
check your
answers!!!!
§ **There may be extraneous
solutions**
Algebra II
4
1. 1− x = 7
2. 3 5x +1 = −4
( 1− x )2 = (7)2
( 3 5x +1)3 = (−4)3
1− x = 49
−x = 48
x = −48
Algebra II
5x +1 = −64
5x = −65
x = −13
5
14
3.
2x + 6 = 10
4
14
2x = 4
4
4
2x = 16
( 4 2x )4 = (16)4
2x = 65536
x = 32768
Algebra II
4. 2 3 13x − 5 = 10
3
13x − 5 = 5
( 3 13x − 5 )3 = (5)3
13x − 5 = 125
13x = 130
x = 10
6
5. x − 7 = x − 5
(x − 7)2 = ( x − 5)2
2
x −14x + 49 = x − 5
2
x −15x + 54 = 0
(x − 6)(x − 9) = 0
x=6
6.
3
486 − 27x 3 = 3x
( 3 486 − 27x 3 )3 = (3x)3
486 − 27x 3 = 27x 3
486 = 54x 3
9=x
x=9
3
Algebra II
3
9=x
7
7. 4 x +1 = x +1
1
1
x +1 = x +
4
4
1
1 2
2
( x +1) = ( x + )
4
4
1 2 1
1
x +1 = x + x +
16
8
16
1 2 1
1
16[x +1 = x + x + ]
16
8
16
16x +16 = x 2 + 2x +1
0 = x 2 −14x −15
0 = (x −15)(x +1)
x = 15 x = −1
Algebra II
8
8.
2x + 2 − 3 x +1 = 0
2x + 2 = 9x + 9
2x + 2 = 3 x +1
2
( 2x + 2 ) = (3 x +1)
−7x = 7
2
x = −1
2x + 2 = 9(x +1)
Algebra II
9
9. 2 − 4 2x − 6 = 14
10. omit
− 4 2x − 6 = 12
4
2x − 6 = −12
( 4 2x − 6 )4 = (−12)4
2x − 6 = 20736
2x = 20742
x = 10371
Algebra II
10
1 52
11. x = 16
2
7
12. (6x +10) 3 + 28 = 156
1 52
2( x = 16)
2
x
5
5
2
2
= 32
(x ) = (32)
2
5
x=4
Algebra II
2
5
7
(6x +10) 3 = 128
7
3
((6x +10) ) = (128)
6x +10 = 8
3
7
3
7
6x = −2
−1
x=
3
11
Algebra II
12
Algebra II
13
1. 3√x – 4 = -2
3√x = 2
(3√x)3 = (2)3
x = 8
Check: 3√8 – 4 = -2
2 – 4 = -2
-2 = -2
Algebra II
2. 2x3/2 + 2 = 252
2x3/2 = 250
2x3/2 = 250
2
2
x3/2 = 125
(x3/2)2/3 = (125)2/3
x = 25
Check:
2(25)3/2+2 = 252
252 = 252
14
3. 5 – 4√x = 0
- 4√x = -5
- 4√x = -5
-1
-1
(4√x)4 = (5)4
x = 625
Check:
5 – 4√625 =0
5 – 5 = 0
0=0
Algebra II
4. √4x – 7 + 2 = 5
√4x – 7 = 3
(√4x – 7) 2 =(3)2
4x – 7 = 9 4x = 16
x = 4
Check:
√4(4) – 7 + 2 = 5
√16 – 7 = 3
√9 = 3
3 = 3
15
5. √3x + 2 – 2√x = 0 6. x – 4 = √2x
(x – 4)2 = (√2x)2
√3x + 2 = 2√x x2 – 8x + 16 = 2x
(√3x + 2)2 = (2√x )2 x2 – 10x + 16 = 0
3x + 2 = 4x
(x – 8)(x – 2) = 0
2 = x
x= 8
x = 2
Check: 8 – 4=√2(8) 2–4 =√2(2)
√3(2) + 2 – 2√2 = 0 Algebra II
4 = √16
-2 =√4
4 = 4 True! -2 = 2 False!
x = 8 is the only solution to
16
the equation. 7. 2x1/4 + 2 = 10
Algebra II
8. √2x + 8 – 4 = 6
17
9. √4x + 28 – 3√2x = 0
Algebra II
10. x + 2 = √2x + 28
18
11. √12 – 2x – 2√x = 0
Algebra II
12. x – 3 = √4x
19
Solve each: 1. 5x1/5 – 2 = 8
2. X + 2 = √8x + 1
3. 2√x – 4 = -2
4. √ 2x – 3 – 4√x = 0
Algebra II
20