After the formula of equation x2-3x + P = 0, we get (x + m) 2 = 12. (1) find the value of constant P and m; (2) find the root of the equation

After the formula of equation x2-3x + P = 0, we get (x + m) 2 = 12. (1) find the value of constant P and m; (2) find the root of the equation

(1) ∵ x2-3x + P = 0, ∵ x2-3x = - P, x2-3x + (32) 2 = - P + (32) 2, (x-32) 2 = - P + 94, ∵ M = - 32, - P + 94 = 12, the solution is: P = 74, M = - 32; (2) ∵ x2-3x + P = 0, ∵ x-32) 2 = 12, x-32 = ± 22, that is, the solution of the equation is: X1 = 3 + 22, X2 = 3 − 22

Given that the points a (- 2,0), B (0,2) and C are the moving points on the circle x2 + y2 = 1, the minimum area of △ ABC is___ ．

From the meaning of the question, we can get the minimum area of △ ABC required by ab = 22, as long as we find the minimum distance d from C to the straight line ab. because the distance from O to the straight line AB: X-Y + 2 = 0 is 2  Dmin = 2-1, the minimum area of △ ABC is 22 (2-1) × 12 = 2-2, so the answer is: 2-2

Let p be the moving point on the parabola y ^ 2 = 2px, pass through p to make two tangent lines of the circle C (x-2p) ^ 2 + y ^ 2 = P ^ 2, and the tangent points are a and B respectively. Then the minimum value of PACB of the quadrilateral is obtained

As shown in the figure, in square ABCD, M is the midpoint of CD, e is a point on CD, and ∠ BAE = 2 ∠ dam

Prove: as shown in the figure, extend AB to F, make BF = CE, connect EF and BC to intersect at point n. in △ BFN and △ Cen, ∠ FBN = ∠ C = 90 °∠ BNF = ∠ cnebf = CE, ｜ △ BFN ≌ △ cen (AAS), ｜ BN = CN, EN = FN, and