solve sqrt 2x-1 =x-2 . !!!!!!!!!!!!!!!

Question

check for extraneous solutions

Answer 1

√(2x-1)=x-2

Squaring on both sides

2x-1=(x-2)^2

2x-1=x^2-4x+4

x^2-6x+5=0

x^2-5x-x+5=0

x(x-5)-1(x-5)=0

(x-5)(x-1)=0

x=(1,5)