Solve the problem a + B + C = 1 x + y + Z = 9 and find the maximum value of T = ax + by + CZ

t=ax+by+cz

Given that a ≠ B ≠ C and (B-C) / x = (C-A) / y = (a-b) / Z, we prove that ax + by + CZ = 0

Let (B-C) / x = (C-A) / y = (a-b) / z = K
Because a ≠ B ≠ C, K ≠ 0
Then B-C = KX AB AC = Kax
c-a=ky bc-ab=kby
a-b=kz ac-bc=kcz
AB AC + BC AB + AC BC = K (AX + by + CZ)
So K (AX + by + CZ) = 0
So ax + by + CZ = 0

Solve the problem a + B + C = 1 x + y + Z = 9 and find the maximum value of T = ax + by + CZ

Solve the problem a + B + C = 1 x + y + Z = 9 and find the maximum value of T = ax + by + CZ

Given that a ≠ B ≠ C and (B-C) / x = (C-A) / y = (a-b) / Z, we prove that ax + by + CZ = 0

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