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,

Let k = ax ^ 3 = by ^ 3 = CZ ^ 3, then ax ^ 2 / k = 1 / x, by ^ 2 / k = 1 / y, CZ ^ 2 / k = 1 / Z1 / x + 1 / y + 1 / z = 1, that is: ax ^ 2 + by ^ 2 + CZ ^ 2 = k = ax ^ 3 = by ^ 3 = CZ ^ 3 (AX ^ 2 + by ^ 2 + CZ ^ 2) ^ (1 / 3) = k ^ (1 / 3) = x * a ^ (1 / 3) = y * B ^ (1 / 3) = Z * C ^ (1 / 3) a ^ (1 / 3) + B ^ (1 / 3) + C ^ (1 / 3) = k ^ (1 / 3) * (1 / x + 1 / 3

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1. Given that (a ^ 2) + (b ^ 2) + (C ^ 2) = 1, (x ^ 2) + (y ^ 2) + (Z ^ 2) = 1, prove: ax + by + CZ
2. (x ^ 2 + y ^ 2 + Z ^ 2) (a ^ 2 + B ^ 2 + C ^ 2) = (AX + by + CZ) ^ 2 to prove X / a = Y / b = Z / C
3. Let x-by + CZ, y = CZ + ax, z = ax + by, find the value of a / A + 1 + B / B + 1 + C / C + 1
4. 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
5. 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
6. 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
7. 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
8. 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
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