i think this is Binomial Theorem

the integer just grater than (√3+1)^6

15 Answers

106
Asish Mahapatra ·

Its (√3 +1)^6 + (√3 - 1)^6

11
Subash ·

yes asish but how please explain

62
Lokesh Verma ·

Subash look closely..
The answer itself gives the hint!

62
Lokesh Verma ·

what can u say aobut the expression that asish added to the original one?

11
Subash ·

i dont get it :(

62
Lokesh Verma ·

is that expression less than 1??

And is the sum an integer?

11
Subash ·

is it the first terms conjugate

11
Subash ·

i get it that the second term is<1

but basically how did we get that term

62
Lokesh Verma ·

that is a tough one to answer... I mean it comes with practice subash...

It is like mroe the problems (or types) you have seen in the past.. more you can apply...

Now these kind of questions will be solvable by u too in the future... wont they :)

11
Subash ·

will be certainly

now another one

integer just less than (2+√3)^5

13
MAK ·

This is an explanation for d first question asked by u...

(rt.3+1)^6 = I + f .......... integral + fractional part...

let F = (rt.3-1)^6 ....... F < 1

I+F+f=2(I').................... I' is an integer... observe...

since RHS is an integer, LHS should also be an integer ...... => F+f must be an integer

=> f+F=1.......... (since sum of two fractional parts cannot be ≥2)

hence to get an integer juzz greater than I+f, we must add 'F'...

hope its clear now... [1]

13
MAK ·

similarly for second one... v can say d ans is (2+rt.3)^5 - (2-rt.3)^5... [1]

11
Subash ·

thanx mak clear ho gaya

11
Subash ·

second answer is wrong shud i post the ans or will u try again

13
MAK ·

sorry for d wrong ans... [2]

i'll try it tomorrow... dont post d answer atleast for others...

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