If the line y = x + 3 and the parabola y = - x + 2x + 3 intersect at two points a and B, the area of the triangle with a, B and origin 0 as the vertex is obtained No picture, step, high score

If the line y = x + 3 and the parabola y = - x + 2x + 3 intersect at two points a and B, the area of the triangle with a, B and origin 0 as the vertex is obtained No picture, step, high score

From the intersection of the straight line y = x + 3 and the parabola y = - x ^ 2 + 2x + 3 at two points a and B, we can get x + 3 = - x + 2x + 3, x-x = 0, x = 0 or x = 1. When x = 0, y = 3; when x = 1, the intersection point of y = 4 is a (0,3) and B (1,4) ‖ the abscissa of B point BX = 1 ‖ s △ OAB = 1 / 2 × OA × BX = 1 / 2 × 3 × 1 = 3 / 2