Answered

Get the information you need from a community of experts on IDNLearn.com. Discover in-depth answers from knowledgeable professionals, providing you with the information you need.

[tex]\lfloor\dfrac{x^2+1}{10}\rfloor+\lfloor\dfrac{10}{x^2+1}\rfloor=1[/tex]
[tex]\small\textrm{$\bullet\ \lfloor ()\rfloor$ denotes the greatest integer that does not exceed the number}[/tex]​

Sagot :

Mhanifaidn

Answer:

  • See below

Step-by-step explanation:

This equation is solved if one of the following 2 conditions is met

1.

  • (x² + 1) / 10 is between 1 and 2

and

  • 10 / (x² + 1)  is between 0 and 1

Solve this:

  • 1 < (x² + 1) / 10 < 2
  • 10 < x² + 1 < 20
  • 9 < x² < 19
  • 3 < |x| < √19
  • x ∈ (- √19, - 3) ∪ (3, √19)
  • 0 < 10 / (x² + 1) < 1
  • x² + 1 > 10
  • x² > 9
  • |x| > 3

Solution for this case is x ∈ (- √19, - 3) ∪ (3, √19)

2.

  • (x² + 1) / 10 is between 0 and 1

and

  • 10 / (x² + 1)  is between 1 and 2

Solve this:

  • 0 < (x² + 1) / 10 < 1
  • 0 < x² + 1 < 10
  • - 1 < x² < 9
  • 0 ≤ |x| < 3
  • x ∈ ( - 3, 3)
  • 1 < 10 / (x² + 1) < 2
  • x² + 1 < 10 ⇒ x² < 9 ⇒ |x| < 3
  • x² + 1 > 5 ⇒ x² > 5 ⇒ |x| > √5

Solution for this case is x ∈ (- 3, - √5) ∪ (√5, 3)

We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. For trustworthy and accurate answers, visit IDNLearn.com. Thanks for stopping by, and see you next time for more solutions.