9514 1404 393

**Answer:**

n = 8

**Step-by-step explanation:**

"By inspection" is an appropriate method.

We are asked to compare the expressions

**n**·n

**8**·n

and find the value(s) of n that makes them equal. <em>By inspection</em>, we see that **n=8** will make these expressions equal. We also know that both expressions will be zero when **n=0**.

__

More formally, we could write ...

n^2 = 8n . . . . the two formulas give the same value

n^2 -8n = 0 . . . . rearrange to standard form

n(n -8) = 0 . . . . . factor

Using the zero product rule, we know the solutions will be the values of n that make the factors zero. Those values are ...

n = 0 . . . . . makes the factor n = 0

n = 8 . . . . . makes the factor (n-8) = 0

Generally, we're not interested in "trivial" solutions (n=0), so the only value of n that is of interest is **n = 8**.

__

A lot of times, I find a graphing calculator to be a quick and easy way to find function argument values that make expressions equal.