Question

For each positive integer n, which of the following is also a square number (a perfect square)?
a. n2 + 2n + 2 b. n2 + 8n + 4
c. n2 + 4n + 2 d. n2 + 2n + 1

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Answer 1

Answer:

(d)

Step-by-step explanation:

(a)

${n}^{2} + 2n + 2 = {n}^{2} + 2n + 1 + 1 \\ = {(n + 1)}^{2} + 1$

It is not a perfect square.

(b)

${n}^{2} + 8n + 4 = {n}^{2} + 4n + 4 + 4n \\ = {(n + 2)}^{2} + 4n$

It is also not a perfect square.

Similarly (c) is not a perfect square

(d)

${n}^{2} + 2n + 1 = {(n + 1)}^{2}$

It is a perfect square.

Answer 2

Explanation:

Answer is (d).