Let a and B be two real numbers. How to compare the sizes of a and B?
Let a and B be two real numbers. How to compare the sizes of a and B
When A-B = 0, a = B;
When A-B > 0, a > B;
When A-B < 0, a < B;
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- 1. a. B, C ∈ positive real number, a ^ 2 + B ^ 2 = C ^ 2. When n ∈ n, n > 2, please compare the size of C ^ n and a ^ n + B ^ n thank you
- 2. Verification: for any real number a and B, there is │ a + B │ ≤ │ a + │ B │. (hint: for any real number a, there is - │ a │ ≤ a ≤ │ a │)
- 3. We know that a and B are positive real numbers, and prove that: (a + b) × (1 / A + 1 / b) ≥ 4
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- 7. Let a, B ∈ R, and a + B = 1. Prove: (a + 2) 2 + (B + 2) 2 ≥ 252
- 8. If a + B = 1, a and B are all positive real numbers, prove: (a + 1 / a) ^ 2 + (B + 1 / b) ^ 2 > = 25 / 2
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- 11. It is known that a and B are real numbers, and a, B = 3, a + B = 4 1, general points, A-1 points of a + 1, B-1 points of B + 1 2. Try to find the value of a + 1 of A-1
- 12. We know that a is a real number, a = a ^ 2 / (a ^ 4 + 1), B = a ^ 4 / (a ^ 6 + 1), compare the size of a and B I hope it can be explained more clearly
- 13. It is known that A. B belongs to real number r. compare a ^ 4 + B ^ 4 with (a ^ 3) B + (b ^ 3) a?
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- 15. It is known that a is equal to 2 times a minus a plus nine fourths, B is equal to 2 times a plus one. For any real number a, compare the size of a and B
- 16. Given that a and B are real numbers, the size of a ^ 2 + B ^ 2 and ab is Do you know the situation
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- 18. If a and B are real numbers, compare a ^ 2 + B ^ 2 with ab
- 19. For any positive real numbers a and B, the size relation between (a ^ 2 + B ^ 2) / 2 and ab is studied For any positive real number a, B, the size relation with AB is studied (1) Substituting the numerical value, comparing the size, finding the law ① When a = 3, B = 1, (a ^ 2 + B ^ 2) / 2 > AB; ② When a = root 3, B = root 3, (a ^ 2 + B ^ 2) / 2___ ab; ③ a=___ ,b=___ (a ^ 2 + B ^ 2) / 2___ ab; Conjecture: for any positive real number a, B, (a ^ 2 + B ^ 2) / 2___ ab. (2) Construct graph to verify conjecture The algebraic formula (a ^ 2 + B ^ 2) / 2 can be expressed by the sum of the areas of two isosceles right triangles whose waist length is a and B respectively. The above conjecture can be verified by means of the splicing and segmentation of the two triangles (3) Application Explore: the maximum area of a right triangle with a hypotenuse of 5
- 20. The difference between integer, real number, natural number and rational number? What are integers and include 0? What is a real number and does it include circular decimals? What are rational numbers and irrational numbers? What is natural number and whether it includes 0