![](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>)
Let a, B, C and d be real numbers, and find the values of 2007a + 5B + 8C / 2007x + 5Y + 8Z Let a, B, C, d be real numbers. If the square of a + the square of B + the square of C = 25, the square of X + the square of Y + the square of Z = 36, ax + by + CZ = 30, find 2007a + 5B + 8C / 2007x + 5Y + 8Z, what is the value?
When a, B and C are real numbers, there are innumerable solutions to this problem
I think the condition of this problem should be that a, B, C, x, y and Z are integers
In this way, we can get the following conclusions
A^2+B^2+C^2=25.(1)
X^2+Y^2+Z^2=36.(2)
AX+BY+CZ=30.(3)
(1) + (2) - 2 * (3) obtained: 1
(A-X)^2+(B-Y)^2+(C-Z)^2=1.（4）
(1) + (2) + 2 * (3) we get the following results
(A+X)^2+(B+Y)^2+(C+Z)^2=121.（5）
It can be seen from formula (4) that in the case of integer, there must be two terms of 0 and the other term of 1
Then let a = x, B = y, C = Z + 1, or C = Z-1 solve C = 5, z = 6, or C = - 5, z = - 6, other values are 0,
So the value of the formula is 5 / 6
RELATED INFORMATIONS
- 1. Given ax ^ 3 = by ^ 3 = CZ ^ 3,1-x + 1-y + 1-z, What's the size relationship between the root sign (AX ^ 2 + by ^ 2 + CZ ^ 2) and the root sign a + B + C
- 2. Ax * 3 (the third power of x) = by * 3 = CZ * 3, and 1 / x + 1 / y + 1 / z = 1. Prove (AX * 2 + by * 2 + CZ * 2) * 1 / 3 = a * 1 / 3 + b * 1 / 3 + C * 1 / 3, How to solve this kind of problems,
- 3. Given that (a ^ 2) + (b ^ 2) + (C ^ 2) = 1, (x ^ 2) + (y ^ 2) + (Z ^ 2) = 1, prove: ax + by + CZ
- 4. (x ^ 2 + y ^ 2 + Z ^ 2) (a ^ 2 + B ^ 2 + C ^ 2) = (AX + by + CZ) ^ 2 to prove X / a = Y / b = Z / C
- 5. Let x-by + CZ, y = CZ + ax, z = ax + by, find the value of a / A + 1 + B / B + 1 + C / C + 1
- 6. It is known that {x = 1, {y = 2, {z = 3, are the solutions of the equations {ax + by = 2, {by + CZ = 3, {CX + AZ = 7, and the value of a + B + C is obtained
- 7. If the solution of the system of equations ax-by-2z = 13, ax + 2Y + CZ = - 2, cx-4y + BZ = 28 is x = 3, y = - 1, z = - 2, find the value of a, B, C
- 8. Given a ^ 2 + B ^ 2 + C ^ 2 = 1, x ^ 2 + y ^ 2 + C ^ 2 = 9, find the maximum value of AX + by + CZ The answer is 3
- 9. Given a & sup2; + B & sup2; + C & sup2; = 1, X & sup2; + Y & sup2; + Z & sup2; = 1, prove ax + by + CZ ≤ 1 It's easy to understand
- 10. If the solutions of the equations ax by = 8, cy BZ = 1, 2bx + CZ = 5 are x = 1, y = - 2, z = - 1, then what is the number of ABC
- 11. What is the condition that a is greater than or equal to minus 16 and less than or equal to 0
- 12. Given the two roots of the quadratic equation AX square plus B x plus C equal to zero, this paper proves that ax square plus B x plus C equals a (x minus x1) (x minus x2)
- 13. Given the function f (x) = x square - ax + A / 2 (x is greater than or equal to 0 and less than or equal to 2), if a ∈ R, find the minimum value of F (x)
- 14. Given that f (x) = the square of ax, (a > 0) when 0 is less than or equal to X and less than or equal to 1, find the minimum value of F (x)
- 15. Let a, B, x, y ∈ R and satisfy A2 + B2 = m, X2 + y2 = n, the maximum value of AX + by is ⊙___ ．
- 16. Given x + y = m, a + B = n, then the maximum value of AX + by is?
- 17. Let a, B, x, y ∈ R and satisfy A2 + B2 = m, X2 + y2 = n, the maximum value of AX + by is ⊙___ ．
- 18. X = - 3, the absolute value of y = 5, Z + 3 = 0, find the value of xy-yz + XZ
- 19. It is known that the opposite number of X is 3, the absolute value of Y is 4, and the sum of Z and 3 is 0. Find the value of XY + YZ + XZ
- 20. Given that the opposite number of X is - 3, the absolute value of Y is 0, and the reciprocal of Z is - 1 / 3, try to find the value of XY + YZ + XZ