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

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Answer 1 · 2016-08-27T18:28:57

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

The eqn. has no extraneous soln.

#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.