IIT JEE , AIEEE Forum - Mathematics , Algebra - Fractional part sum...:.:.:.::.:.:>easy one>...>..>

Ronaldooo

If (3

3 +5)¹¹=p+f where p is an integer and f is a proper fraction then the value of f(p+f) is????
Plzz solve this...i can only see one method,i.e,the expansion of the term and then separating root terms...but that is way too time consuming...plzzz any other method??

prateekdhariwal

solve it by integral part of binomial expression....

Ronaldooo

What???It may be too easy to say for you but not for me to understand...can you elaborate???

sandeepramesh

actually i think the question might be different :) The general technique for these sums is to take the conjugate of the given expression and then find it to be <1 and declare it as the fraction

Ronaldooo

No,sandeep,i am sure about the question.Answer is 2¹¹.Can anyone please try??

elastiboysai

theres a genl result for such questions:

ans is 2^11

$\text{There is a standard result}\\ if (\sqrt{A}+B)^n=I+f\\ \text{where I and n are integers, n being odd and} 0<f<1\\ (I+f)\cdot f=k^n\\ where A-B^2=k\ and \sqrt A-B<1$

sandeepramesh

okie, here's a start. Consider A = (3sqrt(3)-5)^11 .

B = (3sqrt(3)+5)^11

Add A - B = integer clearly and 1> A >0 clearly.

So B is the fractional part :)

So (p+f) is B and f is A so answer is 2^11 :)

EDIT: Sorry didnt see elasti posted

elastiboysai

As for the proof of this result, Rohit a.k.a Sandeep is rite.

Consider the conjugate of the expression,

Subtract both --that shud be an integer,

now do some jugglery , multiply both n get this result

edit : rohit has already gvn the rite method

sboosy

Ronaldooo

Thanks sandeep,elasti and sboosy for helping me out...

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