00:01
In this problem, we have been given two sets, and we need to show that they are equal.
00:05
So first of all, let us consider that x belongs to a.
00:09
Now, if we consider the definition of the set a, the set a is the set of all elements x, says that x squared minus 4x plus 4 is equal to 1.
00:21
So if x belongs to a, it will satisfy this equation.
00:24
Now, the left -hand side, we can write that as x squared minus 2 times 2 times x plus 2 squared.
00:32
So that's a squared minus 2 a b plus b squared, which is a minus b whole square.
00:37
So this is x minus 2 whole squared.
00:40
This is equal to 1.
00:42
And that will imply that x minus 2 is equal to plus or minus the square root of 1, which is 1.
00:49
So x minus 2 is equal to 1 or x minus 2 is equal to negative 1.
00:59
So from here we get that x is equal to 1 plus 2 which is 3 and here we have x is equal to negative 1 plus 2 which is 1.
01:07
So x is 3 or x is 1 and that will imply that x belongs to b because b has the elements 1 and 3.
01:15
So if x belongs to a then x belongs to b.
01:18
Next let us consider that x belongs to b...