Question

A. Show all of your work to solve each equation and to check for extraneous solutions:1.  [√(x - 3)] - 7=0

Answer 1

Given:

`(√(x-3))-7=0`

Required:

We need to find the value of x.

Step-by-step explanation:

Set x =28 and substitute in the equation.

`(√(28-3))-7=0`

`(√(25))-7=0`

`5-7=0`

`-2=0`

This is not true.

x=28 is an extraneous solution.

Set x =39 and substitute in the equation.

`(√(39-3))-7=0`

`(√(36))-7=0`

`6-7=0`

`-1=0`

This is not true.

Set x =52 and substitute in the equation.

`(√(52-3))-7=0`

`(√(49))-7=0`

`7-7=0`
`0=0`

This is true.

x=52 is the solution.

Final answer:

`x=52`