sqrt of x-1=x-3?

Answer 1

√(x-1) = x - 3

square both sides

x - 1 = (x - 3)²
x - 1 = x² - 6x + 9
0 = x² - 7x + 10
0 = (x-5)(x-2)
x = 5 or x = 2

but check, since squaring both sides can introduce extraneous solutions.

√(5-1) = √4 = 2 = 5 - 3 ....... OK
√(2-1) = √1 = 1 <> -1 = 2 - 3 .... not OK

so x = 5.

Answer 2

sqrt(x-1)=x-3
or,x-1=(x-3)^2 [squaring both sides]
or,x-1=x^2-6x+9
or,x^2-6x+9-x+1=0
or,x^2-7x+10=0
or(x-2)(x-5)=0
therefore,either x-2=0 or x-5=0
If x-2=0,then x=2
If x-5=0,then x=5
or,x=2 or 5 ans

Answer 3

square both sides:
x-1=x^2-6x+9
x^2-7x+10=0
x=2,5 answer