As shown in the figure, in a-bcd, e and F are the midpoint of AB and CD respectively. Try to compare the size of EF and 12 (AD + BC) and prove your conclusion

As shown in the figure, in a-bcd, e and F are the midpoint of AB and CD respectively. Try to compare the size of EF and 12 (AD + BC) and prove your conclusion

As shown in the figure, take the midpoint g of AC and connect Ge, GF, Ge is the median line of △ ABC; GF is the median line of △ ACD, de = 12bc, GF = 12ad, Ge + GF = 12 (AD + BC). In △ GEF, from the triangle trilateral relationship, we can get Ge + GF ﹥ EF ﹥ 12 (AD + BC) ﹥ EF

In the space quadrilateral ABCD, ad = BC = 2, e and F are the midpoint of AB and CD respectively. If EF = 3, the angle of AD and BC on the different plane is calculated

Let G be the midpoint of AC, ∵ E and f be the midpoint of AB and CD respectively ∥ eg ∥ BC and eg = 12bc = 1fg ∥ ad, and FG = 12ad = 1 ∥ EGF be the angle (or its complementary angle) formed by the out of plane lines AD and BC ∵ EF = 3, ∥ EGF, cos ∥ EGF = − 12 ∥ EGF = 120 °, that is, the angle formed by out of plane lines AD and BC is 60 °

Extend the line AB to C, make BC = 2Ab, then extend Ba to D, make ad = 3AB, find the relationship between DC and AB, DC and BC, DB and AB, BD and BC
Please write the process

The drawing shows that DC = Da + BC + AB = 6ab
Because BC = 2Ab, DC = 6ab, DC = 3bC
DB=DA+AB=3AB+AB=4AB
Because BD = Da + AB = 3AB + AB = 4AB, BC = 2Ab, so BD = 2BC

If the three numbers a, B and C form an equal ratio sequence, and the common ratio q = 3, and a, B + 8 and C form an equal difference sequence, find the three numbers

Let a be x, then B be 3x and C be 9x
2 * (B + 8) = a + C
That is, 2 * (3x + 8) = x + 9x
That's 6x + 16 = 10x
That's 4x = 16
That's x = 4
So a = 4, B = 12, C = 36

For four numbers, the first three numbers form an equal ratio sequence, and their sum is 19, and the last three numbers form an equal difference sequence. What is their 12? What are the four numbers

If the sum of the last three numbers is 12, then the third number = 12 ／ 3 = 4, if the common ratio of the first three numbers is Q, then the second number is 4 / Q, and the first number is 4 / Q & # 178; 4 / Q & # 178; + 4 / Q + 4 = 194 / Q & # 178; + 4 / Q = 1515q & # 178; - 4q-4 = 0 (5q + 2) (3q-2) = 0q = - 2 / 5 or q = 2 / 3. When q = - 2 / 5, 4 / Q = 4 /

The product of three numbers is 512. If the first number and the third number are subtracted by 2 respectively, they will be equal difference series. Find the three numbers

Let three numbers be a, B, C in turn. According to the meaning of the question, ABC = 512 ∵ the three numbers form an equal ratio sequence, ∵ B2 = AC, ∵ B3 = 512, B = 8. Let the common ratio of the three numbers be t, then a = 8t, C = 8t. The first number and the third number are reduced by 2 respectively. The later number sequence becomes 8t-2, 8, 8t-2 ∵ the new number sequence becomes an equal difference number sequence ∵ 16 = 8t-2 + 8t-2. Arrange 2t2-5t + 2 = 0, obtain t = 2 or 12. When t = 2, a = 4, C = 16, the three numbers are 4, 8, 16 When t = 12, a = 16, C = 4, the three numbers are 16, 8, 4

The product of three numbers is 512. If the first number and the third number are subtracted by 2 respectively, they will be equal difference series. Find the three numbers

Let three numbers be a, B, C in turn. According to the meaning of the question, ABC = 512 ∵ three numbers form an equal ratio sequence, ∵ B2 = AC, ∵ B3 = 512, B = 8. Let the common ratio of three numbers be t, then a = 8t, C = 8t, the first number and the third number are reduced by 2 respectively, and the latter sequence becomes 8t-2, 8, 8t-2 ∵ the new sequence becomes an equal difference sequence ∵ 16 = 8t-2 + 8t-2

The product of three numbers is 512. If the first number and the third number are subtracted by 2 respectively, they will be equal difference series. Find the three numbers

Let three numbers be a, B, C in turn. According to the meaning of the question, ABC = 512 ∵ three numbers form an equal ratio sequence, ∵ B2 = AC, ∵ B3 = 512, B = 8. Let the common ratio of three numbers be t, then a = 8t, C = 8t, the first number and the third number are reduced by 2 respectively, and the latter sequence becomes 8t-2, 8, 8t-2 ∵ the new sequence becomes an equal difference sequence ∵ 16 = 8t-2 + 8t-2

The product of three numbers is 512. If the first number and the third number are subtracted by 2 respectively, they will be equal difference series. Find the three numbers

Let three numbers be a, B, C in turn. According to the meaning of the question, ABC = 512 ∵ three numbers form an equal ratio sequence, ∵ B2 = AC, ∵ B3 = 512, B = 8. Let the common ratio of three numbers be t, then a = 8t, C = 8t, the first number and the third number are reduced by 2 respectively, and the latter sequence becomes 8t-2, 8, 8t-2 ∵ the new sequence becomes an equal difference sequence ∵ 16 = 8t-2 + 8t-2

The product of three numbers is 512. If the first number and the third number are subtracted by 2 respectively, they will be equal difference series. Find the three numbers

Let three numbers be a, B, C in turn. According to the meaning of the question, ABC = 512 ∵ the three numbers form an equal ratio sequence, ∵ B2 = AC, ∵ B3 = 512, B = 8. Let the common ratio of the three numbers be t, then a = 8t, C = 8t. The first number and the third number are reduced by 2 respectively. The later number sequence becomes 8t-2, 8, 8t-2 ∵ the new number sequence becomes an equal difference number sequence ∵ 16 = 8t-2 + 8t-2. Arrange 2t2-5t + 2 = 0, obtain t = 2 or 12. When t = 2, a = 4, C = 16, the three numbers are 4, 8, 16 When t = 12, a = 16, C = 4, the three numbers are 16, 8, 4