Download Review for Test #4 Solve by Extraction of Roots method (Square

Math 0310
Review for Test #4
Solve by Extraction of Roots method (Square Root method):
1) 5 x 2  2  0
2) ( 4 x  3) 2  12
3) (3 x  7) 2  36
Solve by completing the square:
4) x 2  6 x  10  0
5) x 2  10 x  106  0
6) 3 x 2  5 x  4  0
Solve by quadratic formula:
7) 6 x 2  8 x  1  0
8) 3 x 2  2(1  3 x)
9) 8 x 2  x  2
Solve rational equations:
10)
1
7
3
 2

x 1 x  x  2 x  2
11)
3x  2 6 x  2

2x  3 4x 1
12)
x
3
8

 2
x  2 3x  2 3x  4 x  4
Solve radical equations and check:
13)
3 x  7  5  10
14)
x7  x5
15)
2x
2
 7 x  21
3
2
 125
Find the solutions of the following problems.
16. The sum of the squares of two consecutive odd integers is 202. Find the integers.
17. The area of a rectangle is 40 square inches. The width of the rectangle is 2 inches less than
twice the length. Find the width and length of the rectangle.
18. The area of a triangle is 8 square inches. The base of a triangle is 1 inch less than 5 times
the height. Find the height. Round answers to 2 decimal places.
19. Elmer can paint his house in 4 days. Elmer can paint the house in 12 days. Working
together, how long will it take them to paint the house?
20. Gary takes 15 hours to clean the house. With his wife’s help, they can clean it in 3 hours.
How long would it take his wife to clean the house alone?
21. The sum of the reciprocals of two consecutive even integers is
22. The sum of a number and its reciprocal is
13
. Find the integers.
84
13
. What is the number?
6
Answers.
1)
 10
i;
5
2)
3 2 3
;
4
12) x = 1
13) x 
14) x  3
1
15) x   , 4
2
1 13
3) x   ,  ;
3 3
16. Numbers: -11, -9 or 9, 11
4) x   19 +3 17. Width = 5 inches, Length = 8 inches
5) x  5  9i 18. Height:
5
23
5  23 i
6) x   
i or x 
; 6
6
6
7) x 
4  10
6
1 3 7

i or
16 16
10) x = 1
11) x 
.
4
;
33
1  321
 1.89
10
19. Working together: 3 hrs
20) Wife:
15
3
hrs or 3 hrs;
4
4
21)* Numbers: 12, 14.
3  15
8) x 
3
9) x 
32
;
3
x
1  3i 7
;
16
*Note: Calculations on test won’t be this big
as in #21
22) Numbers:
3
2
and .
2
3
Review Test #4 Math 0310