Question

How do you solve the equation `sqrt(5r-1)=r-5`?

Answer 1

`r=13`

Explanation:

As we have `sqrt(5r-1)=r-5`, domain of `r` is `[1/5,oo)`

Squaring both sides in `sqrt(5r-1)=r-5` we get

`5r-1=(r-5)^2`

or `5r-1=r^2-10r+25`

or `r^2-15r+26=0`

or `r^2-13r-2r+26=0`

or `r(r-13)-2(r-13)=0`

or `(r-2)(r-13)=0`

i.e. `r=2` or `13`

Observe that both values are within domain but `r=2` results in `sqrt(5r-1)=sqrt9=3!=2-5`, as it takes negative square root of `sqrt(5r-1)` for equality to hold.

Hence, answer is `r=13`.