What is the largest value of k such that the equation 6x - x^2 = -4x + k has at least one real solution?
6x - x² = k
=> x² - 6x + k = 0,
For there to be at least 1 real solution,
The discriminant b² - 4ac must be at least 0.
We have (-6)² - 4(1)(k) >= 0.
Therefore 36 - 4k >= 0, k <= 9.
Hence the largest value of k is 9.