There is a mathematical problem: a natural number a, a total of 10 divisors, including 1 and a, to find the product of these divisors

The fifth power of a

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1. Given a + B + C = 0, prove AB + BC + AC = 1
2. In △ ABC. Ab ⊥ AC, ad ⊥ BC in D, the proof: 1 / ad ^ 2 = 1 / AB ^ 2 + 1 / AC ^ 2 So in the tetrahedral ABCD, what kind of conjecture can you get by analogy with the above conclusion, and explain the reason
3. It is known that plane α and β satisfy α⊥ β, α∩ β = L, straight line AB is in plane α, ab ⊥ L, straight line BC and de are in plane β, and BC ⊥ de. the proof is AC ⊥ De
4. Given △ ABC, linear L ⊥ AB, l ⊥ AC, prove L ⊥ BC
5. In the triangle ABC, BC = a, AB + AC = L, make a vertical line from the bisector of the outer angle a 'of the angles B and C, and prove that BD * AE = fixed value with the perpendicular feet of D and E
6. It is known that a + B + C = 2,0
7. Given a + B + C = 0, AB + BC + AC = 0, prove a = b = C = 0
8. Prove that a ^ 2 + B ^ 2 + C ^ 2-ab-ac-bc is a nonnegative number
9. If we know the square of a + the square of B + the square of C - AB BC AC = 0, we can judge the size relation of ABC quickly
10. In △ ABC, ∠ ABC = 90 degrees, D, E on AB, ad = AC, be = BC, try to judge whether the size of ∠ DCE is related to the size of ∠ B, if so, ask for the relationship between them, determine the degree, and explain the reason wait anxiously A |\E | D C -----------B Can't upload graphics, so that means. I hope I can understand it. A. B and C are △ and there are lines from e to C and D to C respectively.
11. The natural number n has 45 positive divisors. The minimum value of n is______ ．
12. How many positive divisors does 75600 have? How many odd divisors? Point out the ideas, thank you!
13. The divisor of 120, All divisors of 120 (except 1) are written as the product of prime factors of 120
14. Is there a point Q on the positive half axis of the x-axis for the motion of the moving point P on the ellipse with the equation x ^ 2 / 9 + y ^ 2 / 4 = 1, so that the shortest distance between the point on the trajectory equation of Q and P is 1? If there is, find the Q coordinate. If not, explain the reason
15. 1. The A.B.C of the ellipse is known to be an equal ratio sequence, and the eccentricity is calculated 2. If the endpoint of the minor axis of the ellipse and the two focal points form an isosceles right triangle, calculate the eccentricity
16. On ellipses The coordinates of two fixed points a and B of triangle ABC are respectively - 6060. The product of the slope of the straight line where AC BC is located is equal to - 9 / 4. Find the trajectory equation of fixed point C
17. It is known that the center of the ellipse is at the origin and the focus is on the x-axis. The area of the quadrilateral obtained by connecting its four vertices is 42. Connect a point on the ellipse (except the vertex) and the four vertices of the ellipse respectively. The product of the slopes of the four straight lines where the line segment is located is 14. The standard equation of the ellipse is obtained
18. 2 times (a quadratic + B quadratic + C quadratic) > a quadratic (B + C) + B quadratic (a + C) + C quadratic (a + b) Here's a picture of you. You can see it more clearly
19. 1、 Let the vector OA = (3, - root 3), OB = (COS a.sin a), where 0 is less than or equal to a, less than or equal to two-thirds, if the vector AB = root 13, find the value of Tan A / find the maximum area of triangle AOB two, known sequence {an} is the equal ratio sequence of first term A1 = 1, and an ＞ 0, {BN} is the arithmetic sequence of first term 1, and A5 + B3 = 21, A3 + B5 = 13, find the general term formula of {an} {BN}, Finding the first n terms and Sn of sequence {molecule BN denominator 2An}
20. Let the point P (5.2) F1 (- 6.0) F2 (6.0) be p ` F1 ` F2 'respectively with respect to the symmetrical point of the straight line y = x, and find the standard equation of the hyperbola with the focus of F1 ` F2' and passing through the point P '.