AIME Algebra

Question 1

Find the sum of all real values of x satisfying x^4 - 5x^2 + 4 = 0.

Accepted Answer

0

Answer

2

Answer

4

Answer

5

Question 2

If a + b = 5 and ab = 3, what is a^3 + b^3?

Accepted Answer

80

Answer

95

Answer

110

Answer

65

Question 3

The system 2x + 3y = 7 and 4x + ky = 14 has infinitely many solutions when k equals:

Accepted Answer

6

Answer

3

Answer

7

Answer

4

Question 4

If f(x) = x^2 + 2x + 1 and g(x) = x - 1, find f(g(3)).

Accepted Answer

4

Answer

9

Answer

16

Answer

1

Question 5

What is the product of all solutions to (x-2)^2 = 9?

Accepted Answer

-5

Answer

5

Answer

13

Answer

-13

Question 6

If log_2(x) + log_2(x-2) = 3, find x.

Accepted Answer

4

Answer

2

Answer

8

Answer

6