It is known that the sum of the three positive numbers in the arithmetic sequence is equal to 15, and the three positive numbers are added with 9 in turn, then they are in the arithmetic sequence, and the three positive numbers are solved

It is known that the sum of the three positive numbers in the arithmetic sequence is equal to 15, and the three positive numbers are added with 9 in turn, then they are in the arithmetic sequence, and the three positive numbers are solved

The middle number of arithmetic sequence is 15 / 3 = 5, so let the three numbers be 5-D, 5,5 + D
After adding 9 is: 14-d, 14,14 + D, into an equal ratio sequence
(14-d)(14+d)=14^2
D = 0
So the original three numbers are: 5,5,5

For any positive integer k and positive number C (C is less than or equal to 3), there is (s (K + 1) - C) / (sk-c)

What is SK, the sum of the first k terms of the sequence? Suppose that SK is the sum of the first k terms of the sequence, that is, SK = 2 [1 - (1 / 2) ^ k] / [1 - (1 / 2)] = 4-4 * (1 / 2) ^ k; s (K + 1) = 4-4 * (1 / 2) ^ (K + 1) = 4-8 * (1 / 2) ^ k; according to the meaning of [4-c-8 * (1 / 2) ^ k] / [4-c-4 * (1 / 2) ^ k] 0 → C

It is known that three positive numbers form an arithmetic sequence, and their sum is equal to 9. If these three numbers are added with 1, 1 and 3 respectively, the three numbers obtained form an arithmetic sequence in turn
Find the original number

Let the first number be x and the tolerance be y, x + (x + y) + (x + 2Y) = 9, (x + y + 1) (x + y + 1) = (x + 2Y + 3) (x + 1)
X + (x + y) + (x + 2Y) = 9 to get x + y = 3, then substitute it to get 5x + xy = 3, and the solution is x = 1 or x = 7
When x = 1, y = 2, then the original number is 1,3,5
When x = 7, y = - 4, then the original number is 7,3, - 1

Given that the three sides of a triangle form an equal ratio sequence, how to find the value range of their common ratio

If the side length of triangle is greater than 0 and the common ratio q is greater than 0, let the three sides be a / Q, a, AQ in turn
The sum of the two sides of the triangle > the third side, the difference between the two sides aq
a/q+aq>a
a+aq>a/q
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q²-q0 (2)
q²+q>1 (3)
(1)：(q-1/2)²

A and B drive from a to B at the same time. Four hours later, B arrives at B and exceeds a by 56 kilometers. It is known that a travels 80 kilometers per hour, and B travels how many kilometers per hour?

(80 × 4 + 56) △ 4, = (320 + 56) △ 4, = 376 △ 4, = 94 (km / h). Answer: car B travels 94 km per hour

Ask for a mathematical inequality (basic problem) in grade one of senior high school,
Let a, B and C be the three sides of triangle ABC, and prove that a / (B + C-A) + B / (a + C-B) + C / (a + B-C) ≥ 3

According to the variation of Cauchy inequality a / (B + C-A) + B / (a + C-B) + C / (a + B-C) = a ^ 2 / a (B + C-A) + B ^ 2 / b (a + C-B) + C ^ 2 / C (a + B-C) > = (a + B + C) ^ 2 / [a (B + C-A) + B (a + C-B) + C (a + B-C)] = (a + B + C) ^ 2 / [2 (AB + BC + Ca) - (a ^ 2 + B ^ 2 + C ^ 2)] = (a + B + C) ^ 2 / {(AB + BC + Ca) - [(a-b) ^ 2 + (b) ^ 2) = (a + BC + Ca) = (a + C) = (a + B + C) ^ 2 / {(a + b) = (a + b) ^ 2) = (a + C-B) = (a + b)

A. the two vehicles left a and B at the same time and met at a distance of 15 km from the midpoint three hours later. It is known that the speed of a is 80% of that of A
How many kilometers are there between the two places?

Suppose the speed of car B is x km / h, then the speed of car a is 80% x km / h, the equation can be listed: 3 (80% x) + 15 = 3x-15, the solution is x = 50, when x = 50, 2 × (3x-15) = A: the distance between the two places is 270 km
Or use ratio: A: B = 80%: 1 = 4:5
Distance between two places: (15 + 15) / (5-4) x (5 + 4) = 270 (km)
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Given two vectors a = (3,4), B (2,1), if (a + XB) ⊥ (a-b), then x equals () a, - 3 B, 3 / 2 C, 3 D, - 2 / 3

If the inner product of two vectors is 0, the condition of perpendicularity is that the product of the corresponding coordinates of two vectors is equal to 0
2*-4+（-1）*2+3x=0,
If the corresponding terms of the two vectors are proportional to each other, we can get parallel (XY two coordinate axes have been given, they must be proportional, otherwise they cannot be parallel), then 2 / (- 4) = (- 1) / 2 = 3 / x, and x = - 6
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For two baskets of apples with the same kilogram, basket a sells 7 kilogram. After basket B sells 19 kilogram, the remaining kilogram of basket a is three times that of basket B. how many kilogram of apples were there in each basket?

(x-7)/(x-19)=3
x-7=3x-57
x=25

Given that I vector and j vector are unit vectors in the positive direction of X and Y axes respectively, and point C is on the unit circle with o as the center, OC vector = Xi + YJ, find the maximum value of X + y

Because x ^ 2 + y ^ 2 = 1,
So from (x + y) ^ 2 = x ^ 2 + y ^ 2 + 2XY