Home
Class 12
MATHS
If in a positive integer such that If a ...

If in a positive integer such that If a number a=p+f whre p is an integer and `0ltflt1`. Here p is called the integral part of a and f its fractional part. Let `n in N` and `(sqrt(3)+1)^(2n)=p+f`, where p is the integral part and `0ltflt1`. On the basis of bove informationi answer teh following question:
The integral part p of `(sqrt(3)+1)^(2n)` is
(A) an even number for al n epsilon N
(B) an odd number for all nepsilon N
(C) anodd or even number according as n is odd or even
(D) an even or odd nuber according as n is odd or even

Text Solution

AI Generated Solution

Promotional Banner

Similar Questions

Explore conceptually related problems

If in a positive integer such that If a number a=p+f whre p is an integer and 0ltflt1 . Here p is called the integral part of a and f its fractional part. Let n in N and (sqrt(3)+1)^(2n)=p+f , where p is the integral part and 0ltflt1 . On the basis of bove informationi answer teh following question: f^2+(p-1)f+4^n= (A) p (B) -p (C) 2p (D) -2p

Integral part of (7 + 5sqrt2)^(2n+1) is (n in N)

Integral part of (7 + 4sqrt3)^n is (n in N)

Show that the integral part of (5 sqrt(5) + 11)^(2n +1) is even where n in N .

If n is a positive integer and (3sqrt(3)+5)^(2n+1)=l+f where l is an integer annd 0 lt f lt 1 , then

If n and p are positive integers such that 8(2^(p))=4^(n) , what is n in terms of p?

Show that the integral part of (5 + 2 sqrt(6))^(n) is odd where n is natural number

If (8 + 3sqrt(7))^(n) = P + F , where P is an integer and F is a proper fraction , then

If m and p are positive integer and (2sqrt(2))^(m)=32^(n) , what is the value of (p)/(m) ?

If (3sqrt(3)+5)^n=p+f. where p is an integer and f is a proper fraction. then find the value of (3sqrt3-5)^n,nin,N, is