Give an example of a radical equation for which all solutions are extraneous.

Question

What is the solution to the equation? How do you know? 

Answer 1

 

NOTE ... SQRT = square root

 

SQRT( 4x + 5 ) + 1 = 0

 

SQRT (4x + 5) = -1

 

Square both sides

 

4x + 5 = (-1)²

 

4x = 1 - 5

 

4x = -4

 

x = -1

 

Check for extraneous solution:

 

SQRT( 4(-1) + 5 ) + 1 = 0

 

SQRT(1) + 1 = 0

 

1 + 1 = 0

 

2 = 0

 

FALSE

 

No solution!