Question 989398
sqrt ( 2x-3 ) - sqrt ( x-2 ) = 1
add sqrt ( x-2 ) to both sides of =
sqrt ( 2x-3 ) = 1 + sqrt ( x-2 )
square both sides of =
2x-3 = 1 +2sqrt (x-2) + x-2
x-2 = 2sqrt (x-2)
square both sides of =
x^2-4x+4 = 4x -8
x^2 -8x +12 = 0
(x-6)(x-2) = 0
x = 6 or x = 2
**********************************
check the answers in the original equation
1) x = 6
sqrt(2*6-3) - sqrt(6-2) = 1
3 -2 = 1
1 = 1
answer checks
2) x = 2
sqrt(2*2-3) - sqrt(2-2) = 1
1 - 0 = 1
1 = 1