Solution is confusing

Loki123

Full Member
Joined
Sep 22, 2021
Messages
790
Hey,
In the first picture I have the problem and how I solved it. The second picture is how the solution is. While our final answers match, the solution for the second case (which I marked as II and they marked as 2.) does not. Is this my fault or theirs?
242988808_194917112729037_4117489400032661764_n.jpg12.3. book.png
 
Hey,
In the first picture I have the problem and how I solved it. The second picture is how the solution is. While our final answers match, the solution for the second case (which I marked as II and they marked as 2.) does not. Is this my fault or theirs?
View attachment 29031View attachment 29032
In case 2, you forgot to exclude solutions that do not satisfy the condition, x < 0! Only [imath](-\infty,-1/6][/imath] does; [imath][1,+\infty)[/imath] must be dropped (from that case).
 
You should also understand that
\(\displaystyle \sqrt{x^2+ 8}\le 2+ x\)
does NOT necessarily imply
\(\displaystyle x^2+ 8\le (2+ x)^2\)

Squaring both sides of an inequality may change the inequality.
For example, -4< -2 but16 is NOT less than 4!
 
The point is that the equation you asked about is not a differential equation. It was a plain old algebraic equation. In a differential equation, the unknown is a differentiable function rather than a number.

This question is one that might be asked in a college algebra class or early in a differential calculus course. It would have been perfectly appropriate under either Intermediate Algebra or Calculus.

We ask people to try to find a sensible category, but the real difficulty with posting in an inappropriate category is that you may wait a long time for any response.
 
The point is that the equation you asked about is not a differential equation. It was a plain old algebraic equation. In a differential equation, the unknown is a differentiable function rather than a number.

This question is one that might be asked in a college algebra class or early in a differential calculus course. It would have been perfectly appropriate under either Intermediate Algebra or Calculus.

We ask people to try to find a sensible category, but the real difficulty with posting in an inappropriate category is that you may wait a long time for any response.
Okay, thank you. I will post in the right category from now on.
 
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