If-lim-x-a-x-2-bx-4b-x-a-6-find-a-and-b-

Question Number 125575 by ZiYangLee last updated on 12/Dec/20

If \lim_{x \to a} \frac{x^{2} - b x + 4 b}{x - a} = - 6, find a and b .

Answered by ajfour last updated on 12/Dec/20

a^{2} - a b + 4 b = 0

2 a - b = - 6

\Rightarrow a^{2} + (2 a + 6) (4 - a) = 0

\Rightarrow a^{2} - 2 a - 24 = 0

\Rightarrow {(a - 1)}^{2} = 25

\Rightarrow a = 1 \pm 5

(a, b) \equiv (6, 18), (- 4, - 2)

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