Question

Find the set of values of x satisfying the equality [3/4] + [4/3] = 5, where [,] = G..I.F belongs to the interval ( a, b/c], where a, b, c are natural number and b/c is in its lowest forms. Find the value of a + b + c + abc + 30. 

Answer 1

Given equation is [3/x] + [4/x] = 5

when x is negative, the value of [3/x] + [4/x] can never be equal to 5 when x is positive, there are 3 possibilities

This is not possible simultaneously,

So, it has no solution.

From (ii), [3/x] = 1, then 1 ≤ 3/x < 2

This is not possible simultaneously,

So, it has no solution. 

From (iii), we get,

Thus, a = 1, b = 4, c = 3

Hence, the value of a + b + c + abc + 30

= 1 + 4 + 3 + 12 + 30 = 50.