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Hi iamaditya,(really it is false;it is you who is aditya)
Suppose only first and second equations are given with a,b,c as positive integers. Can you evolve a method to find the numbers? Not purely hit and try method (Ram bharosa method) but with some logic in it.
hi evene,
Can you check the nth term by substituting n=1,2,3 etc.?
O.K. I may be wrong.
You mean permutation or combination?
I have not given the answer. It was you.That is only one way thinking.One could think in other ways also like a problem of combinations only.
hi dazzle,
Have you realized there are infinite number of circles meeting the criterion but product of y coordinates remaining constant?
In (2) first term ab is clear ;second and third terms have c common i.e.c(a+b)=c(10-c). i hope you can simplify further.
The nth term of the serie should be
First ensure remainder is zero and then use long division.
discriminant a^2-4b>0 but 4a>-4b So a^2+4a>0 i.e. a^2+4a+4>4; (a+2)^2>4 which means |a+2|>2
I think my hint did not provoke you.
Lay them side by side with common side. Same height and equal base. Proved.
In (1) Put v=ut ;u can be written in terms of t but t itself is v/u.
For (2) What is wrong with
Leave the first term. Others are in Geometric progression.Sum them up and you get the result.
I think in Q.3 there is something missing. What exactly is ths? \frac 1{x_1}+\frac 1{x_2}<1
evene's interpretation does not seem to be what is intended or something is missing.
Probably m=n=1 and t=1 may be the minimum restraints to make them equal,unless it is considered trivial.
In need help with solving
for m in terms of n,s,t.How do I evaluate this? (Note that I mostly need help with the actual algebra part)