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We know that: (a + b + c) 2 = a 2 + b 2 + c 2 + 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 + B 2 C 2
= 2 2 + (√3) 2 * (√2) 2 = 4 + 6 = 10
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