How do you solve #sqrt(2x-4) = x-2# and find any extraneous solutions?

1 Answer
Aug 27, 2016

Answer:

Thus, the Soln. is #x=2, or, x=4#

The eqn. has no extraneous soln.

Explanation:

#sqrt(2x-4)=x-2#.

#:. {sqrt(2x-4)}^2=(x-2)^2#.

#:. 2(x-2)=(x-2)^2#.

#:. 2(x-2)-(x-2)^2=0#

#:. (x-2)(2-x+2)=0#

#:. (x-2)(4-x)=0#

#:. x=2, or, x=4#.

These roots satisfy the given Eqn.

Thus, the Soln. is #x=2, or, x=4#

The eqn. has no extraneous soln.