Let the real number x, y satisfy the equation 2x2 + 3y2 = 4x, find the minimum value of X + y

Let the real number x, y satisfy the equation 2x2 + 3y2 = 4x, find the minimum value of X + y


Let x + y = k, then K-X = y, substituting into the original formula, have
2X ^ 2 + 3 (K-X) ^ 2 = 4x, which is reduced to 5x ^ 2 - (4 + 6K) x + 3K ^ 2 = 0,
If the discriminant is greater than or equal to 0, then (4 + 6K) ^ 2-60k ^ 2 > = 0, and finally we can get an inequality about K, which can find the minimum value
Wuwuwuwuwuwuwuwuwu, I missed 15 minutes, ah