IIT-JEE
Calculus
Level
2
The Set of real values of x satisfying the equality [3/x]+[4/x] = 5 (where [.] denotes the greatest integer function) belongs to (a, b/c] where a, b, c are natural numbers and b/c is in lowest form. Find the value of a + b + c + abc.
25
15
20
10
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1 solution
Suppose that x>1, to get 5 its needed to add two positive integers bcz ∀x>1,(⌊3x⌋<⌊4x⌋).
So its obvious that only integer that satisfy the condition (2,3) or (1,4), However for the
Second couple its not find Corrosponding x, bcz to have ⌊3x⌋=1 necessary x>32 and together with the values ⌊4x⌋=4⇒x<1 Gives an empty set
Analyse Situation when ⌊3x⌋=2 and ⌊4x⌋=3 So we get 2≤3x≤3 and 3≤4x≤4 so solution x∈(1,43]