Let m = {0,1}, N + {11-A, LGA, 2 ^ A, a}, whether there is a real number a, such that M intersects n = {1}

Let m = {0,1}, N + {11-A, LGA, 2 ^ A, a}, whether there is a real number a, such that M intersects n = {1}

If M ∩ n = {1}, then there must be element 1 in n
(1) If 11-A = 1, a = 10. In this case, LGA = LG10 = 1, the element will repeat. Therefore, 11-A cannot be 1
Similarly, LGA cannot be 1
(2) If 2 ＾ a = 1, then a = 0, then there are both elements 1 and 0 in the set n, and m ∩ n = {0,1} does not conform to the known condition
2 ＾ a cannot be 1
(3) If a = 1, then LGA = 0. M ∩ n = {0,1}
To sum up, there is no such real number a

If there is a real number a in the set a = {a, a + 1}, B = {1,2, B}, (1), then for any real number B, there is a intersection B = a
(2) If a ∪ B = B, find the value of real numbers a and B

(1) A ∩ B = a, a is a subset of B,
If a = 1, B ≠ 1 or 2
(2) A ∪ B = B, a is a subset of B,
When a = 1, B ≠ 1 or 2; when a = 2, B = 3; when a = 0, B = 0

The focus of the ellipse x ^ 2 / 9 + y ^ 2 / 4 = 1 is F1, F2, and the point P is the moving point on it. When the angle f1pf2 is an obtuse angle, the abscissa range of point P is

F1 (- radical 5,0) F2 (radical 5,0)
Let P (3cosx, 2sinx)
Then vector Pf1 = (3cosx + radical 5,2sinx) vector PF2 = (3cosx - radical 5,2sinx)
Vector Pf1 * vector PF2 = 9 (cosx) ^ 2-5 + 4 (SiNx) ^ 2 = 5 (cosx) ^ 2-1

The focus F1 and F2 of ellipse x2 / 9 + Y2 / 4 = 1, and the point P is the moving point. When the angle f1pf2 is an obtuse angle, the abscissa range of point P is
The focus F1 and F2 of ellipse x2 / 9 + Y2 / 4 = 1, and the point P is the moving point. When the angle f1pf2 is an obtuse angle, the abscissa range of point P is

Method 1: make a circle with the diameter of F1F2, work out its equation, and work out the intersection point together with the elliptic equation. Let the intersection point above the horizontal axis be a and B respectively, and the abscissa be a and B respectively (let a > b). Then, when point P moves to a or B, from the knowledge of the circle, we can get that f1pf2 is a right angle, so when p is in the elliptic part between AB, f1pf2 is an obtuse angle, so the value range of abscissa of P is (B, a) AB can be obtained by equations
Method 2: let the abscissa of p be x, then the distance from it to two focal points is a + ex, a-ex, f1pf2 is obtuse angle, cosf1pf2 = Pf1 ^ 2 + PF2 ^ 2-f1f2 ^ 2 / 2pf1 * PF2