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The number of positive integral values of x satisfying the equation [x/13] = [x/17] is n, where [⋅] denotes the greatest integer function, then n/3 is equal to
Correct answer is '9'. Can you explain this answer?
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The number of positive integral values of x satisfying the equation [x...
[x] represents the greatest integer less than or equal to x. We can rewrite the equation as follows:
[x/13] = [x/17]
This equation can be rewritten as:
13([x/13]) = 17([x/17])
13([x/13]) = 17([x/13] + [x/17])
13([x/13]) = 17([x/13] + 1)
13([x/13]) = 17([x/13]) + 17
-4([x/13]) = 17
([x/13]) = -17/4
Since the greatest integer less than or equal to -17/4 is -5, there are no positive integral values of x satisfying the equation. Therefore, n = 0.
[x/13] = [x/17]
This equation can be rewritten as:
13([x/13]) = 17([x/17])
13([x/13]) = 17([x/13] + [x/17])
13([x/13]) = 17([x/13] + 1)
13([x/13]) = 17([x/13]) + 17
-4([x/13]) = 17
([x/13]) = -17/4
Since the greatest integer less than or equal to -17/4 is -5, there are no positive integral values of x satisfying the equation. Therefore, n = 0.
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Community Answer
The number of positive integral values of x satisfying the equation [x...
x ∈ {1, 2, ..., 12}, x ∈ {17, 18, ..., 25}
x ∈ {34, 35, ..., 38} and x = {51}
∴ Total number of solutions = 27
∴ n/3 = 9
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The number of positive integral values of x satisfying the equation [x/13] = [x/17] is n, where [⋅] denotes the greatest integer function, then n/3 is equal toCorrect answer is '9'. Can you explain this answer?
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