Question 201392: Solve the inequality
4k^3-6k^3(< or =)4k
possible answers:
(-infinite,-1/2] or (0,2)
(-infinite,-1/2) or (0,2)
(-infinite,-1/2] or [0,2]
(-infinite,-1/2) or [0,2]
Found 3 solutions by Theo, ikleyn, greenestamps:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! simplify the left side of the equation to get
-2k^3 <= 4k
divide both sides by k to get
-2k^2 <= 4
divide both sides of the equation by -2 to get
k^2 >= -2
take the square root of both sides of the equation to get
k >= square root of (-2)
to prove your answer is correct you need to.
1. let k = square root (-2) and solve. the equation should hold true.
2. let k be > than square root (-2) and solve. the equation should hold true.
3. let k be < than square root (-2) and solve. the equation should be false.
Answer by ikleyn(53304)  (Show Source):
You can put this solution on YOUR website! .
Solve the inequality
4k^3-6k^3 <= 4k
possible answers:
(-infinite,-1/2] or (0,2)
(-infinite,-1/2) or (0,2)
(-infinite,-1/2] or [0,2]
(-infinite,-1/2) or [0,2]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
To this problem, I'd like to make two comments.
First comment is that the input is given incorrectly: the given inequality is INCONSISTENT with the answers list.
Second comment is that the solution by tutor @Theo is incorrect.
It contains so dangerous errors that are a mortal threat to an inexperienced and gullible reader.
For example, @Theo considers inequality
-2k^3 <= 4k (*)
and instructs a reader to divide it by 'k' to get
-2k^2 <= 4. (**)
But inequalities (*) and (**) are not equivalent, because if 'k' is negative,
then the inequality sign in (**) must be reversed.
Actually, I do understand perfectly, how the problem should be modified to make it consistent,
but I will not do it.
Why ? - Because (1) I do not understand why I should worry about it more than the visitor,
whose direct duty and direct responsibility is to provide a proper input,
and (2) because it would be too much to make corrections and then to solve the problem.
It would be a bad method to teach - the result will be a person, who is not familiar with the notion of responsibility.
Answer by greenestamps(13241)  (Show Source):
|
|
|
