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Question

Number of values of natural numbers n1 such that n3+3n2+7 is also an integer is

A
1
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B
2
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C
3
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D
4
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Solution

The correct option is B 2

We may write
n3+3n2+7=77n3n2+7
So, n3+3n2+7 is an integer if and only if 7n3n2+7 is an integer.
Now 7n3n2+77nn27n1 if n7.
Tabulating the values of 7n3n2+7 for n=1,2,,6 we get that for n=2 and n=5 only 7n3n2+7 is an integer being equal to 1.
Thus n2+3n3+7 is the integer 21=1 or 51=4 when n=2 or n=5 respectively.

Hence two valus of n satisfy the reqiored condition.


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