Expert: Richard J. Raridon - 6/9/2009

Question
1. Solve:
n^4 - 2n^2 - 8 = 0


2. Solve:  
c^3 + c^2 - 7c - 3 = 0, given root -3


3. Solve:
y^4 - 3y^3 - 2y^2 + 10y - 12 = 0, given root 1 + i


4. Choose the real solutions of the system:
x^2 + 2y^2 = 12 and 3x^2 - y^2 = 8


5. Choose the real solution of the system:
9x^2 + 9y^2 = 1 and x = y^2 + 1


6. Choose the real solutions of the system:
2x^2 - y^2 = 7 and xy = 3


7. Choose the real solutions of the system:
x = y^2 + -9 and x - 4y - 12 = 0

 

8. Choose the real solutions of the system:
y^2 = 2x  and  x^2 + y^2 = 8


9. Choose the real solutions of the system:
xy + 6 = 0 and x - y = -5



10. Choose the real solutions of the system:
4x^2 - y^2 + 12 = 0 and x + y = 3


11. Choose the real solution of the system:
8x^2 + y^2 = 25 and 8x^2 - y^2 = 39

12. Find the length of the legs of a right triangle having perimeter 56m if the hypotenuse is 25m. 12m and 14m  10.5m and 16m


13. Find the dimensions of a rectangle that has area of 10 and a diagonal of length 5.

Answer
1. 2, -2, +/-(-2)^1/2
2. other roots are 1 +/-(2)^1/2
3. 1+i, 1-i, 3,-2
4. x = +/-2, y = +/-2
5. x = 2/3, -5/3
6. x = +/-(3/2)(2)^1/2
7. (40,7), (0,-3)
8. x = 2, y = 4
9. (-2,3),(-3,2)
10. [(1+5^1/2)/3, (8-5^1/2)/3], [(1-5^1/2)/3, (8+5^1/2)/3]
11. x = +/-2
12. 7 and 24
13. 5^1/2, 2(5^1/2)