Question

(x-3)^2=1

Answer 1

find the value of x ??

Answer 2

yes

Answer 3

just square root both sides and you will get x-3 = + or - 1 and just solve for x

Answer 4

apply (a-b)^2= a^2+b^2-2ab
so (x-3)^2= x^2+9-6x
so
(x-3)^2= 1
(x-3)^2-1=0
x^2+8-6x=0
aaply factorisation here
sp
x^2-4x-2x+8=0
(x-4)(x-2)=0
so x=4
and x=2
is the ans :p

Answer 5

A much better way to doing this is move the one to the other side and use difference between two squares.
\[(x-3)^2=1\]
\[(x-3)^2-1=0\]
Using the difference between two squares:
\[\huge (x-a)^2-b^2=[(x-a)-b][(x-a)+b]\]
Using that property, we apply it to your question.:
\[\huge (x-3)^2-1=0\]
\[\huge [(x-3)-1][(x-3)+1]=0\]
\[\huge (x-3-1)(x-3+1)=0\]
\[\huge (x-4)(x-2)=0\]

Answer 6

Now find x.

Answer 7

@jayz657 thank you.
@Azteck

Answer 8

That takes only about 4 lines if compared to other methods.

Answer 9

np glad to help and if you continue on the way i did it
you will have x-3 = 1 and x-3 = -1
so x = 4 and x = 2

Answer 10

Square rooting will become a major problem in further topics of mathematics. Best not to square root equations like this. Square rooting is a danger because you get rid of solutions. It doesn't get rid of solutions here but in other questions, you would of stuffed yourself if you square rooted.

Answer 11

@Luis_Rivera yeah but it asks for two values of x

Answer 12

@Luis_Rivera thank you.