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If a,b,c are in H.P then (3a+2b)/(2a-b) + (3c+2b)/(2c-b) is

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a-Greater then or equal to 10

b-less then or equal to 10

c-only equal to 10

d-non of these

please justify your answer

It's a little hard for people to help you if they don't know quite where you've gone wrong. If you know where you're struggling, then you should mention that. Otherwise, you're basically asking people to give you the answer and that doesn't help anyone, least of all you. Perhaps you could take a photo of your working out if you don't want to type it?

Your question is to abbreviated to understand easily.

 

Does "in H.P." mean in harmonic progression ?

 

Here is a hint :

 

look at the conditions.

 

What other conditions besides a,b,c,d could be stated ?

A few points!

 

1. IMPORTANT and I mean really important. If you expect help you need to put in the time and effort as well.

 

2. Think about what Studiot said and what the only alternative to a,b,c is

 

3. Your workings seem to be based on one particular harmonic progression - is there a reason you have chosen a=1, b=1/2, c=1/3? this is often known as the harmonic series but is not the only possible harmonic progression

 

(and by the way 44/3 does not equal 12)

 

Harmonic Progression

 

This is a progression with terms (the reciprocal of an arithmetic progression) in the form

 

1/k , 1/(k+d), 1/(k+2d), 1/(k+3d),...1/(k+(n-1)d)

 

4. Try substituting in (a=1/k, b=1/(k+d) etc) and simplifying - and you will get a much easier expression. The number 10 pops out which is why it is in the question but there are also other terms

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