Integer part 8

If f(x)=(x^(3)+x+1)tan(pi[x]) (where, [x] represents the greatest integer part of x), then

If x= (8 + 3 sqrt(7))^(n) , where n is a natural number, power that the integral part of x is an odd integer and also show that x - x^(2) + x[x] = 1 , where [.] denotes the greatest integer function .

If [x] and (x) are the integral part of x and nearest integer to x then solve (x)[x]=1

Divide 184 into two parts such that one-third of one part may exceed one-seventh of the other part by 8.

Divide 184 into two parts such that one-third of one part may exceed one-seventh of the other part by 8.

Show that the following integers are cubes of negative integers. Also find the integer whose cube is the given integer. -5832 (ii) -2744000

If 3b+8gt6+2b , and b is a negative integer, what is the value of b?

The product of three consecutive positive integers is 8 times the sum of the three numbers. What is the sum of the three integers?

Write a pair of positive integers, a pair of negative integers, one positive and one negative integer whose: a. sum is -5 " b. " sum is 8 " c. " difference is -7 " d. " difference is 9

Solve : [x]^(2)=x+2{x}, where [.] and {.} denote the greatest integer and the fractional part functions, respectively.