Question

If x² - 2 < 72x, which of the following must be true?

1) x > 2
2) x < -2
3) x > 36
4) x < -36

Answer 1

To solve the inequality x² - 2 < 72x, we can use the quadratic formula x = (-b ± √(b² - 4ac))/(2a), where a = 1, b = -72, and c = -2. The solution is x ≈ -0.028 and x ≈ 72.028. Therefore, the correct option is x < -2.

Step-by-step explanation:

To solve the inequality x² - 2 < 72x, we can rearrange it to x² - 72x - 2 < 0. One way to solve this is by factoring, but it is easier to use the quadratic formula. The quadratic formula is x = (-b ± √(b² - 4ac))/(2a), where a = 1, b = -72, and c = -2 in this case. Solving it, we get x ≈ -0.028 and x ≈ 72.028. So, the correct option is x < -2.