![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
If a, B and C belong to positive real numbers, prove that (a square + 1) (b square + 1) (C square + 1) is greater than or equal to 8abc
a^2+1>=2a
b^2+1>=2b
c^2+1>=2c
So (a square + 1) (b square + 1) (C square + 1) is greater than or equal to 8abc
It is proved that if the square of a plus the square of B divides a by B, a equals B
There is something wrong with the expression. Maybe the square of a plus the square of B can be divided by ab
Let a square + b square = nab
So the square of a is B
The square of B | a
And a and B are integers, so | a | = | B |
It is known that A.B.C is a positive integer. What is the answer to prove that (a b) (b c) (c a) is greater than or equal to 8abc
It is known that A.B.C is a positive integer. What is the answer to prove that (a b) (b c) (c a) is greater than or equal to 8abc
(a b)(b c)(c a)=a²b²c²=(abc)²
(abc)²≥8abc
The answer is ABC ≥ 8
RELATED INFORMATIONS
- 1. In △ ABC, a and B are acute angles. The opposite sides of angles a, B and C are a, B, C, cos2a = 3 / 5, SINB = √ 10 / 10, A-B = √ 2-1 respectively. Find the value of a, B and C
- 2. The definition field of F (x) is known Given the domain [- 2,2], for any x belonging to [- 2,2], there is f (- x) = - f (x), and f (2) = 2. For any m, n belonging to [- 2,2], M + n is not equal to 0, there is f (m) + F (n) / M + n > 0 (1) It is proved that f (x) is an increasing function on [- 2,2] by definition; (2) Solving inequality f (x + 1 / 2)
- 3. If a + B = 10, ab = 7, find the square of (a-b)
- 4. Given a + B = 4N + 2, ab = 1, if the square of 19 + 147ab + 19b is 2009, then n=
- 5. Ab-2a ^ 2B ^ 2 + A ^ 3B ^ 3 AB = - 2
- 6. It is known that | a | = 2, | B | = 4, a > b, ab
- 7. If the rational numbers a and B satisfy | ab-2 | + (1-B) & # 178; = 0; Try to find 1 / AB + (a + 1) (B + 1) 1 / AB + +(a + 2010) (B + 2010) 1 +?
- 8. The rational numbers a and B of (a-b) ^ 2 + (B-A) A-B = AB, (AB ≠ 0) must not satisfy the relation () Selection: 1. AB < 0.2. AB > 0.3. A + b > 0.4. A + B < 0.5
- 9. If AB are all non-zero rational numbers, then a △ | a | + B △ B | =
- 10. 2) Given that a and B are rational numbers and satisfy 2A + 3 √ 3 · b-2-b + √ 3 · A-15 √ 3 = 0, try to find the value of a and B Give reasons
- 11. The three sides of triangle ABC are a, B, C, and they are all positive integers. A > b > C, a = 8, how many such triangles are there the sooner the better
- 12. If the lengths of three sides of triangle ABC are a, B, C and a is less than or equal to B, less than or equal to C, a + B + C = 13, a, B, C are all integers, then there are () triangles with a, B, C as three sides
- 13. In △ ABC, the lengths of three sides are positive integers a, B and C respectively, and B ≥ A. if B = 4 and C = 6, how many triangles are there
- 14. The lengths of three sides of △ ABC are a, B, C respectively, and a > b > C, a, B, C are all positive integers. If the condition 1 / A + 1 / B + 1 / C = 1 is satisfied, the existence of △ ABC can be judged
- 15. If the three sides of △ ABC a, B, C satisfy a + B = 10, ab = 18, C = 8, try to judge the shape of △ ABC
- 16. Let a, B, C be the three sides of the triangle ABC, and satisfy (1) a > b > C; (2) 2B = a + C; (3) A2 + B2 + C2 = 84, then the integer B=______ ．
- 17. Given | a | = 1, | B | = 2, | C | = 3, and a > b > C, find the value of ABC
- 18. Given that a + B + C = 0 and ABC is not equal to 0, calculate the value of a {1 / B + 1 / C} + B {1 / C + 1 / a} + C {1 / A + 1 / b} + 3,
- 19. If a, B and C satisfy a + B + C = 0 and ABC = 8, then the value of 1 / A + 1 / B + 1 / C is () A positive number B negative C zero D nonzero rational number
- 20. It is known that a + B + C = 0, ABC = 8, the square of a + the square of B + the square of C = 32 Connect Find one of a + one of B + one of C We need to be quick