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:

$(\sqrt{x-3})-7=0$

Required:

We need to find the value of x.

Explanation:

Set x =28 and substitute in the equation.

$(\sqrt{28-3})-7=0$

$(\sqrt{25})-7=0$

$5-7=0$

$-2=0$

This is not true.

x=28 is an extraneous solution.

Set x =39 and substitute in the equation.

$(\sqrt{39-3})-7=0$

$(\sqrt{36})-7=0$

$6-7=0$

$-1=0$

This is not true.

Set x =52 and substitute in the equation.

$(\sqrt{52-3})-7=0$

$(\sqrt{49})-7=0$

$7-7=0$$0=0$

This is true.

x=52 is the solution.

Final answer:

$x=52$