Question
If (Ax + By - Cz) 2 Â = 4x 2 Â +
3y 2  + 2z 2  + 4√3xy - 2√6yz - 4√2xz, then find the value of A 2  + B 2 C 2 .Solution
We know that: (a + b + c) 2 Â = a 2 Â + b 2 Â + c 2 Â + 2ab + 2bc + 2ca
(Ax + By - Cz) 2  = 4x 2  + 3y 2  + 2z 2  + 4√3xy - 2√6yz - 4√2xz
(Ax + By - Cz) 2  = (2x) 2  + (√3y) 2  + ( - √2z) 2  + 2 * 2x * √3y + 2 * √3y * ( - √2z) + 2 * 2x * ( - √2z)
(Ax + By - Cz) 2  = (2x + √3y - √2z) 2
After comparing: A = 2, B = √3 and C = √2
Now, A 2 Â + B 2 C 2
= 2 2  + (√3) 2  * (√2) 2 = 4 + 6 = 10
Statements: U = V ≤ W > Q ≥ N; B < Q; E = W
Conclusion: I. E > Q II. W > B
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