Question 87636
{{{(2x-1)^(1/2)=x-2}}}

Squaring both sides, we will get

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

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

Subtract {{{x^2}}} on both sides we will get

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

Add 4x on both sides we will get

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

{{{6x-1 - x^2 = 4}}}

Subtract 4 on both sides we will get

{{{6x-1 - x^2 - 4= 0}}}

{{{- x^2 + 6x - 5= 0}}}

divide by -1 , we will get
{{{x^2 - 6x + 5= 0}}}

Now factorize it

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

x = 5, 1