Question

How do you solve `\sqrt { - 72+ 17n } = n`?

Answer 1

`n = 8" "` or `" "n = 9`

Explanation:

Given:

`sqrt(-72+17n) = n`

First note that `sqrt(...) >= 0` whenever it has a real value. That is, the `sqrt(...)` expression refers to the primary, non-negative square root. Hence any valid solution to the given equation must have `n >= 0`.

Bear this in mind as we square both sides of the equation (potentially introducing extraneous solutions) to get:

`-72+17n = n^2`

Subtract `17n-72` from both sides to get:

`0 = n^2-17n+72 = (n-8)(n-9)`

So:

`n = 8" "` or `" "n = 9`

Both of these are positive and solutions of the original equation.