If 2a + b = 4 and ab = -3, what is the value of |2a - b|?

Answer 1

1. Multiply both sides by a: a(2a + b) = (4)a which is 2a² + ab = 4a
2. Substitute ab = -3: 2a² -3 = 4a
3. Rearrange: 2a² - 4a -3 = 0
4. Solve with quadratic equation: a = 1 + (5/2)^.5, 1 - (5/2)^.5
5. Substitute a to get b = 2 + 10^.5, 2 - 10^.5
6. Substitute the different values of a and b to get the answers: 2, 2 * 10^.5