When lines y=square root by 3x and y=-square root by 3x +6 intersect at point A, and line y=- square root by 3x +6 and the x axis intersect at point B, solve the following problems.

Question

Find the points of intersection A and B.

Answer 1

To find the points of intersection A and B, we first need to set the two equations equal to each other and solve for x and y.

For point A:
√(3x) = -√(3x) + 6
2√(3x) = 6
√(3x) = 3
3x = 9
x = 3

Now plug x = 3 back into one of the original equations to find y:
y = √(3*3) = √9 = 3

So point A is (3, 3).

For point B:
y = -√(3x) + 6
0 = -√(3x) + 6
√(3x) = 6
3x = 36
x = 12

Now plug x = 12 back into the equation to find y:
y = -√(3*12) + 6 = -√36 + 6 = -6 + 6 = 0

So point B is (12, 0).

Therefore, the points of intersection are:
Point A: (3, 3)
Point B: (12, 0)