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Let a be the smallest integer satisfying the inequality x^2 - 15 < 2x + 7x - 40, and let b be the largest integer satisfying the same inequality. What is b-a?

 Jun 21, 2022
 #1
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x^2 - 15 < 2x + 7x - 40      rearrange as

 

x^2 - 9x + 25  <    0      (1)

 

Notice the graph here : https://www.desmos.com/calculator/5gdvkizm7m

 

The graph is always   above the x axis  (always > 0 )  so no x values make (1)  true.

 

 

cool cool cool 

 Jun 21, 2022

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