Question

Let x and y be real numbers such that
x² + y² = 2x - 2y + 2.
What is the largest possible value of x² + y² - √32 ?​

Answer 1

Answer:

x

2

−4x+y

2

+3=0

⇒x

2

−4x+4+y

2

−1=0

(x−2)

2

+y

2

=1

represents a circle with center at (2,0) & radius =1 units

∴x

2

+y

2

≤3

x

2

+y

2

≥1

∴M=3,m=1

∴M+m=4