Let n be a natural number- The number of n-s for which n 4-2 n 3-2 n 2-2 n -1 is a perfect square isA- 2B- 1C- 7D- 0

The correct option is D 0 For N to be a perfect square, since (n+1)2 is already a perfect square, n2 + 1 must be a perfect square. But there is no n (natural ...

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Standard VIII

Mathematics

Square Root of a Number

Let n be a na...

Question

Let n be a natural number. The number of n's for which (n⁴ + 2n³+ 2n² + 2n + 1) is a perfect square is

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Solution

The correct option is D
0

For N to be a perfect square, since (n+1)² is already a perfect square, n² + 1 must be a perfect square.

But there is no n (natural number) such that n² + 1 is a perfect square and hence N is a perfect square for no natural number.

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Let n be a natural number. The number of n's for which (n4 + 2n3 + 2n2 + 2n + 1) is a perfect square is

The correct option is D 0 For N to be a perfect square, since (n+1)2 is already a perfect square, n2 + 1 must be a perfect square. But there is no n (natural number) such that n2 + 1 is a perfect square and hence N is a perfect square for no natural number.

Let n be a natural number. The number of n's for which (n⁴ + 2n³+ 2n² + 2n + 1) is a perfect square is

The correct option is D
0

For N to be a perfect square, since (n+1)² is already a perfect square, n² + 1 must be a perfect square.

But there is no n (natural number) such that n² + 1 is a perfect square and hence N is a perfect square for no natural number.