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JEE Main & Advanced Mathematics Sequence & Series Question Bank Mock Test - Sequences and Series

  • question_answer
    If x, y, z are real and \[4{{x}^{2}}+9{{y}^{2}}+16{{z}^{2}}-6xy-12yz-8zx=0\], then x, y, z are in

    A) A.P                  

    B) G.P.

    C) H.P.                

    D) none of these

    Correct Answer: C

    Solution :

    [c] Multiplying the given expression by 2 and rewriting it, we have \[{{(2x-3y)}^{2}}+{{(3y-4z)}^{2}}+{{(4z-2x)}^{2}}=0\] \[\Rightarrow 2x=3y=4z\] \[\Rightarrow \frac{1}{x},\frac{1}{y},\frac{1}{z}\]are in A.P \[\Rightarrow x,y,z\]are in H.P.


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