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What is the largest value of k such that the equation 6x - x^2 = -4x + k has at least one real solution?

 Jun 15, 2021
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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.

 Jun 16, 2021

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