Answer:
The largest possible value of x is 2 + √8
Explanation:
Given;
x² + y² = 4(x + y)
This is an equation of circle
x² + y² = 4x + 4y
x²- 4x + y² - 4y = 0
complete the square by taking half of coefficient of x and y, then add the squares to both sides;
x²- 4x + (-2)² + y² - 4y + (-2)² = (-2)² + (-2)²
factorize
(x - 2)² + (y - 2)² = √8
This circle has its center at (2, 2) with a radius of √8
The largest x-value occurs at the right end of the circle = x value of the center plus the radius = 2 + √8