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    Question

    If (Ax + By - Cz) 2  = 4x 2  +

    3y 2  + 2z 2  + 4√3xy - 2√6yz - 4√2xz, then find the value of A 2  + B 2 C 2 .
    A 12 Correct Answer Incorrect Answer
    B 10 Correct Answer Incorrect Answer
    C 8 Correct Answer Incorrect Answer
    D 16 Correct Answer Incorrect Answer

    Solution

    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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