Given x + y = 5, x ^ 2 + y ^ 2 = 7, find the value of XY. Given x + y = 4, xy = 3, find the value of x ^ 2 + y ^ 2

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• 1. Given x = 1 / √ 7 - √ 5, y = 1 / √ 7 + √ 5, find the value of x ^ 2 + XY + y ^ 2
• 2. If | x + Y-5 | + (xy-6) ^ 2 = 0, then x ^ 2 + y ^ 2=
• 3. The 96th power of 2 minus 1 can be divided by two integers between 60 and 70
• 4. In the expansion of (1-x ^ 2) (1 + 2x ^ 2) ^ 12, what is the coefficient of x ^ 8? The correct answer is 6160
• 5. Find the coefficient of x ^ 4 in the expansion of (1 + x-2x ^ 2) (x + 1 / x) ^ 8
• 6. Inspired by "shower faucet", Mr. Li made up a topic: intercept the corresponding line AB from 0 to 3 on the number axis, and the real number m corresponds to the point m on AB, as shown in Figure 1; fold AB into an equilateral triangle, so that the points a and B coincide with the point P, as shown in Figure 2; establish a plane rectangular coordinate system, translate the triangle, so that it is symmetrical about the Y axis, and the coordinates of point P are (0,2), PM and X axis intersect at point n (n,0) ）When m = 3, find the value of N. when you solve this problem, the value of n is () A. 4-23B. 23-4C. −233D. 233
• 7. When x = 1, the value of formula (x-1) / 3 is 3 times larger than that of X + 1 / 2
• 8. The teacher gave such a question and compared the product size of the following two formulas: 1] 12345x54321 2] 12344x54322 what's the thinking process
• 9. In the expansion of (1 + 2x-x ^ 2) ^ 4, find the coefficient of x ^ 7?
• 10. Factorization of 2x ^ 3-8x ^ 2 + X + 6 by undetermined coefficient method
• 11. If the square of (x + y) is 7 and the square of (X-Y) is 5, find the value of XY Given the square of X - 2x = 2, find the square of (x-1) + (x + 3) (x-3) + (x-3) (x-1)
• 12. Given that f (x) = 2 / (3 ^ X - 1) + m is an odd function, find the value of the constant M Given that f (x) = 2 / (3 ^ X - 1) + m is an odd function, find the value of the constant M It's the X of three, minus one
• 13. The known function f (x) = x & # 178; + A / X (x ≠ 0), (constant a ∈ R) (1) If f (x) is an even function, find a (2) When the constant a ≤ 16, we prove that the function f (x) increases monotonically on [2, + ∞)
• 14. If the function f (x) = x & # 178; + A / x increases in the interval [2,3], then the value range of constant a It's a process
• 15. The monotone increasing interval of function y = x-ln (5 + x ^ 2) is_____ . The answer is (- ∞, + ∞) How to calculate? If you take the derivative of Y, you should get - 2x / (5 + x ^ 2), so that the derivative is greater than 0, and you get X
• 16. The following function, which is an increasing function in the interval (0, + ∞), is () A. y=ln（x+2）B. y＝−x+1C. y＝(12)xD. y＝x+1x
• 17. Given f (2x + 1) = 8x + 74x2 + 4x + 2, find the range of F (x)
• 18. 1. Given that f (x + 2) = 4x ^ 2 + 4x + 3 (x belongs to R), then the range of function f (x) is]
• 19. Given the function f (x) = √ 3sin (2x + φ), if f (a) = √ 3, then the relationship between F (a + 5 π / 6) and f (a + π / 12) is?
• 20. Given the function f (x) = 3sin (KX / 5 + π / 3), where k ≠ 0, find the maximum value of the function