To find the intersection points of the two equations, we can set them equal to each other:
x^2 + 2x - 8 = sqrt(x + 2)
Square both sides to eliminate the square root:
(x^2 + 2x - 8)^2 = x + 2
Expand the left side:
(x^2 + 2x - 8)(x^2 + 2x - 8) = x + 2x^4 + 4x^3 - 16x^2 + 4x^3 + 16x^2 - 64x - 8x^2 - 32x + 128 = x + 2x^4 + 8x^3 - 80x + 128 = x + 2x^4 + 8x^3 - 81x + 126 = 0
This is a quartic equation that can be solved to find the values of x. Once we have the values of x, we can substitute them back into either of the original equations to find the corresponding y values.
To find the intersection points of the two equations, we can set them equal to each other:
x^2 + 2x - 8 = sqrt(x + 2)
Square both sides to eliminate the square root:
(x^2 + 2x - 8)^2 = x + 2
Expand the left side:
(x^2 + 2x - 8)(x^2 + 2x - 8) = x + 2
x^4 + 4x^3 - 16x^2 + 4x^3 + 16x^2 - 64x - 8x^2 - 32x + 128 = x + 2
x^4 + 8x^3 - 80x + 128 = x + 2
x^4 + 8x^3 - 81x + 126 = 0
This is a quartic equation that can be solved to find the values of x. Once we have the values of x, we can substitute them back into either of the original equations to find the corresponding y values.