If `(3sqrt3 + 5)^7 = P + F` where P is an integer and F is a proper fraction, then `F(P + F) =`

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

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

If (9 + 4 sqrt(5))^(n) = I + f , n and I being positive integers and f is a proper fraction, show that (I-1 ) f + f^(2) is an even integer.

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 (9+4sqrt(5))^(n)=p+beta , where n and p are positive integers and beta is a positive proper fraction, prrove that (1-beta)(p+beta)=1 and p is an odd integer.

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

If f(x) = px +q, where p and q are integers f (-1) = 1 and f (2) = 13, then p and q are

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

If (2+sqrt(3))^n=I+f, where I and n are positive integers and 0lt f lt1 , show that I is an odd integer and (1-f)(1+f) =1

If f(x) = ax + b, where a and b are integers, f(-1) = -5 and f(3) = 3, then a and b are respectively