Equation with parameter. Help please

But if a=0? Or a=1?

What's with this quadratic equation?

I see now that the inequality you referred to was given by JeffM. (The thread is getting too long to read through easily.) He said it was incomplete, not a final answer. He is also interpreting the question differently than I do, I think.

The main issue is that we can't talk about this without seeing specific work from you! Random questions will not help the discussion along.
 
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No severe translation problems gere
Then why is everyone having such trouble following you? You may be very good at English, but if so, you are not taking the time to use it well.

If we have to find such gaps or values of a, when x=5/6?

This is not a valid question in English. We have two subordinate clauses, but no main clause.

Cannot be that -5/3<a<5/3 cause then, if a =1 means sqrt(5-6x) = NaN
What does NaN mean?

And if a=0 it doesn't satisfy x as well.
"It" lacks an antecedent noun. The sentence as written is therefore defective because unclear.

Your very first post said:

Find all possible a when an equation has only one possible solution.
You have two unknowns in that equation. One possible solution for x? One possible solution for a? You have not even clearly explained the problem.
 
Then why is everyone having such trouble following you? You may be very good at English, but if so, you are not taking the time to use it well.



This is not a valid question in English. We have two subordinate clauses, but no main clause.


What does NaN mean?


"It" lacks an antecedent noun. The sentence as written is therefore defective because unclear.

Your very first post said:


You have two unknowns in that equation. One possible solution for x? One possible solution for a? You have not even clearly explained the problem.



ok. I surrender. Gonna practice my English

well/ Anyways. Let x=5/6

How do I find all possible a's that will satisfy this condition?
 
Then why is everyone having such trouble following you? You may be very good at English, but if so, you are not taking the time to use it well.



This is not a valid question in English. We have two subordinate clauses, but no main clause.


What does NaN mean?


"It" lacks an antecedent noun. The sentence as written is therefore defective because unclear.

Your very first post said:


You have two unknowns in that equation. One possible solution for x? One possible solution for a? You have not even clearly explained the problem.

It is asked all possible values of a for a single x value/ Let it be x=5/6. It may also be x=1/4
 
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I see now that the inequality you referred to was given by JeffM. (The thread is getting too long to read through easily.) He said it was incomplete, not a final answer. He is also wrong about other things, I think (though maybe they are corrected in the additional work he would do).

The main issue is that we can't talk about this without seeing specific work from you! Random questions will not help the discussion along.
I am not sure what was wrong with that answer.

\(\displaystyle x = \dfrac{5}{6} \implies 4x^2 = \dfrac{4 * 25}{36} = \dfrac{25}{9}.\)

\(\displaystyle -\ \dfrac{5}{3} < a < \dfrac{5}{3} \implies 0 \le a^2 < \dfrac{25}{9} \implies -\ \dfrac{25}{9} < -\ a^2.\)

\(\displaystyle \therefore \dfrac{25}{9} - \dfrac{25}{9} < 4x^2 - a^2 \implies 0 < 4x^2 - a^2 \implies ln(4x^2 - a^2) \ \exists.\)

Similarly,

\(\displaystyle x = \dfrac{5}{6} \implies 2x = \dfrac{5}{3}.\)

\(\displaystyle -\ \dfrac{5}{3} < a < \dfrac{5}{3} \implies \dfrac{5}{3} - \dfrac{5}{3} < 2x + a \implies 0 < 2x + a \implies ln(2x + a) \ \exists.\)

If a = 0 and x = 5/6, then

\(\displaystyle \sqrt{5 - 6x} * ln(4x^2 - a^2) = \sqrt{5 - 6x} * ln(2x + a) \implies 0 * ln \left ( \dfrac{25}{9} \right ) = 0 * ln \left ( \dfrac{5}{3} \right ),\)

which is quite obviously true. If a = 1 and x = 5/6, then

\(\displaystyle \sqrt{5 - 6x} * ln(4x^2 - a^2) = \sqrt{5 - 6x} * ln(2x + a) \implies 0 * ln \left ( \dfrac{16}{9} \right ) = 0 * ln \left ( \dfrac{8}{3} \right ),\)

which is also quite obviously true. Moreover, the other restrictions reported by the teacher do not apply in the case of x = 5/6 because as just shown a = 0 works. This suggested to me that the problem was not clearly described, not that the teacher was wrong.
 
It is asked all possible values of a for a single x value. Let it be x=5/6. It may also be x=1/4

Let's figure out what the problem is really saying! You wrote it as,

Find all possible a when an equation has only one possible solution.

I have been taking it to mean,

Find all possible values of the parameter a, such that the equation has only one possible solution for x.

That problem makes sense to me, and I think it yields an answer like what you say it is supposed to be.

What you are saying now doesn't make it a sensible problem. You are taking it to mean, apparently,

Find all possible values of a, given a specific value of x.

No, the value of x can't be intended to be arbitrary, for you to choose.
 
Thank you all for your help. Sorry if I wasted your time...

Anyway, I will report you the final result after a dialogue with my teacher.

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Now I make it clear.

It is said to find all exact values of parameter a, for each of which this equation should have a single solution.

Not sure myself that this phrase is equal to "one and only one possible value of x"

Possibly, this means, that there are many possible x, depending on what is a. But among them, in every single case, this x should be an only solution of an equation?

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If there's still language problem, just ignore please. Don't wanna be annoying

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By the way, NaN = not a number. It is something when we are trying to get square root from negative number. Maybe synonim to indeterminate?

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Now I make it clear.

It is said to find all exact values of parameter a, for each of which this equation should have a single solution.

Not sure myself that this phrase is equal to "one and only one possible value of x"

Possibly, this means, that there are many possible x, depending on what is a. But among them, in every single case, this x should be an only solution of an equation?

It sounds like my interpretation was correct.

Yes, the value of x will depend on the value of a; all you need to make sure of is that, for any a in the set you give as the answer, there will be only one value of x that satisfies the equation.

By the way, NaN = not a number. It is something when we are trying to get square root from negative number. Maybe synonim to indeterminate?

NaN is used in computer programming, and is almost equivalent to "undefined" -- except that it can be used in calculations. "Indeterminate" is slightly different still.

It can be dangerous to mix computer concepts with math. Do you actually call it NaN in your class?

Incidentally, one lesson from all this is that language problems can be very subtle -- it is not only when you don't know a language that you can make mistakes, but especially when you think you know it, but use a slightly wrong word that changes the meaning in a way you wouldn't have imagined!

This is true of native speakers as well as newcomers to the language. An important part of reading is asking for clarification, which we initially failed to do enough; and an important part of writing is to respond to such questions quickly. Also, when you are not sure of your language, it is better to say too much than too little; the more you say, the more easily readers will recognize that something is wrong, and be prompted to ask.
 
In our class we use rather "undefined". But in different language :)

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