Question

How do you solve `sqrt[5x-6]=2` and find any extraneous solutions?

Answer 1

`x=2`

Explanation:

`color(blue)"square both sides"`

`"note that "sqrtaxxsqrta=(sqrta)^2=a`

`(sqrt(5x-6))^2=2^2`

`rArr5x-6=4`

`"add 6 to both sides"`

`5xcancel(-6)cancel(+6)=4+6`

`rArr5x=10`

`"divide both sides by 5"`

`(cancel(5) x)/cancel(5)=10/5`

`rArrx=2`

`color(blue)"As a check"`

Substitute this value into the left side of the equation and if equal to the right side then it is the solution.

`sqrt(10-6)=sqrt4=2=" right side"`

`rArrx=2" is the solution"`

`"There are no extraneous solutions"`