Answer:
The correct solutions are A and B.
Explanation:
To find the solutions to the equation
(
�
−
3
)
2
=
49
(x−3)
2
=49, you can start by taking the square root of both sides:
(
�
−
3
)
2
=
49
(x−3)
2
=
49
�
−
3
=
±
7
x−3=±7
Now, solve for x by adding and subtracting 3 from both sides:
For the positive root:
�
−
3
=
7
x−3=7
�
=
7
+
3
x=7+3
�
=
10
x=10
So, x = 10 is a solution.
For the negative root:
�
−
3
=
−
7
x−3=−7
�
=
−
7
+
3
x=−7+3
�
=
−
4
x=−4
So, x = -4 is a solution as well.
Now, let's check the options:
A. x = 7 - This is a valid solution.
B. x = -4 - This is a valid solution.
C. x = -10 - Not a solution.
D. x = -7 - Not a solution.
E. x = 10 - Not a solution.
The correct solutions are A and B.