Answer:
The length of the segment AB is √48
Explanation:
Given the two equations, the idea is to find the solution to the system
y = x² + 9
y = 2x² - 3
you can use the equality method to find the "x" and "y" of the solution.
x² + 9 = 2x² - 3 ⇒ x² - 2x² = -3 - 9 ⇒ -x² = -12 ⇒ x² = 12 ⇒ x = ±√12.
With this value we return to the original equations and replace it to find "y" values.
y = (±√12)² + 9 ⇒ y = 21
The solutions to the system are (-√12, 21) and (√12, 21). Now you need to find the distance between this points.
d= √[(x2-x1)² + (y2-y1)²] ⇒ d = √48.
The length of the segment AB is √48.