Question 68

In the following question, state whether the statement is True (T) or False (F):

Some of the factors of $\frac{n^{2}}{2} + \frac{n}{2}$ are $\frac{1}{2} n$ and (n+1).

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Solution

True
We have, $\frac{n^{2}}{2} + \frac{n}{2} = \frac{n^{2} + n}{2} = \frac{1}{2} n (n + 1)$
$∴$ The factors are $\frac{1}{2}$ n and (n+1).

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Question 68 In the following question, state whether the statement is True (T) or False (F): Some of the factors of n22+n2 are 12n and (n+1).

True We have, n22+n2=n2+n2=12n(n+1) ∴ The factors are 12 n and (n+1).

Question 68

In the following question, state whether the statement is True (T) or False (F):

Some of the factors of $\frac{n^{2}}{2} + \frac{n}{2}$ are $\frac{1}{2} n$ and (n+1).

True
We have, $\frac{n^{2}}{2} + \frac{n}{2} = \frac{n^{2} + n}{2} = \frac{1}{2} n (n + 1)$
$∴$ The factors are $\frac{1}{2}$ n and (n+1).