The vertex B and C of square ABCD are on the positive half axis of X axis, and a and D are on the parabola y = - 2 / 3x & # 178; + 8 / 3x | Math enthusiast | Mathematical art

The vertex B and C of square ABCD are on the positive half axis of X axis, and a and D are on the parabola y = - 2 / 3x & # 178; + 8 / 3x

Let the side length of a square be a (a > 0), and the abscissa of point a be x, then it is easy to know that the coordinate of a is a (x, a),
The coordinate of D is d (x + A, a). By substituting these two points into the parabolic equation, we can get
-(2 / 3) x & # 178; + (8 / 3) x = a, - (2 / 3) (x + a) &# 178; + (8 / 3) (x + a) = a, then a can be obtained by solving the equations, but this method is a little troublesome
The following method can be used to simplify. The midpoint of the line ad is on the parabola symmetry axis X = 2, so there is [a + (x + a)] / 2 = 2,
The solution is x = 4-2a, substituting - (2 / 3) x & # 178; + (8 / 3) x = a, eliminating x, a can also be obtained. This method can solve a quadratic equation

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