If the square of X + 2 (M-3) x + 49 is a complete square, M =? 3Q

If the square of X + 2 (M-3) x + 49 is a complete square, M =? 3Q

X ^ 2 + 2 (M-3) x + 49 = (x + 7) ^ 2 = x ^ 2 + 14x + 49 or (X-7) ^ 2 = x ^ 2-14x + 49 comparison coefficient M-3 = 7 or - 7 m = 10 or - 4

In order to support farmers to develop agricultural production, the government subsidizes farmers who buy agricultural machinery by 13% of the selling price of agricultural machinery. A city's agricultural machinery company raised 1.3 million yuan to purchase 30 harvesters of a and B models at one time. According to market demand, all these harvesters can be sold, and the profit after all sales is no less than 150000 yuan. Among them, the purchase price and selling price of harvesters are shown in Table 1 The following table: A-type harvester B-type harvester purchase price (10000 yuan / set) 5.33.6 price (10000 yuan / set) 6.4 the company plans to purchase x A-type harvesters, and the company's profit after all the harvesters are sold is y 10000 yuan. (1) try to write the functional relationship between Y and X; (2) what kinds of schemes of purchasing harvesters can the municipal agricultural machinery company choose? (3) What kind of plan to purchase the harvester is the most profitable for the agricultural machinery company? What is the maximum profit? In this case, what is the total amount of government subsidy for all farmers who buy the 30 harvesters?

(1) Y = (6-5.3) x + (4-3.6) (30-x) = 0.3x + 12 (2 points) (2) according to the meaning of the title, there are 5.3x + (30 − x) × 3.6 ≤ 1300.3x + 12 ≥ 15 (4 points), that is, X ≤ 121617x ≥ 10 〈 10 ≤ x ≤ 121617 (5 points) ∵ x is an integer, ∵ x = 10,11,12 (6 points), that is, agricultural machinery companies have three kinds of purchasing and harvesting

For each non-zero natural number n, if the parabola y = x2-2n + 1n (n + 1) x + 1n (n + 1) intersects with the X axis at two points an and BN, and anbn represents the distance between the two points, then A1B1 + a2b2 + +The value of a2009b2009 is______ ．

Y = x2-2n + 1n (n + 1) x + 1n (n + 1) = (x-1n) (x-1n + 1), so the coordinates of the intersection of parabola and X axis are (1n, 0) and (1n + 1, 0) +A2009B2009=（1-12）+（12-13）+… +（12009-12010）=1-12010=20092010．...