Algebra II??

Question

What extraneous solution arises when the equation (squareroot of x+3)=2x is solved for x by first sharing both sides of the equation?

Answer 1

In your written version of this problem, your word SHARING SHOULD HAVE BEEN squaring.

 

Squaring,you get x+3 = 4x² and when you solve 4x²-x-3=0 you get (4x+3 )(x-1) = 0, thus obtaining two possible solutions: 1 & -3/4.

 

Only the value 1 works, the other is extraneous; obviously the left side has to be non-negative but the right side (of orig. equation) would be negative.  

 

-¾ is extraneous.