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Find the smallest integer that satisfies the inequality: (x - 5)(x + 5)(x - 3) > 0.

 Jan 19, 2024
 #1
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(x - 5)(x + 5)(x - 3) > 0

(x^2 - 25)(x - 3) > 0 | : (x - 3)

 

> case 1: if x > 3 (this case as we search the smallest integer)

x^2 - 25 > 0 | + 25

x^2 > 25 | sqrt

x > 5 and -5 > x

 

=> smallest integer: -4

 

(> case 2: if x < 3 (jst ignore; opposite of case 1)

x^2 - 25 < 0 | + 25

x^2 < 25 | sqrt

-5 < x < 5)

 Jan 20, 2024
edited by SomebodySomeone  Jan 20, 2024
 #2
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correction: case 1: -5 < x

 Jan 20, 2024

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